With gasoline prices increasing, drivers are more concerned with their cars’ gasoline consump- tion. For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2. Now that his car is 5 years old, he would like to know whether the variability of gas mileage has changed. He recorded the gas mileage from his last eight fill-ups; these are listed here. Conduct a test at a 10% significance level to infer whether the variability has changed.
28 25 29 25 32 36 27 24
Answers
Answer:
The calculated chi -square value =5.7356 Is less than12.01 at 0.1level of significance .
The null hypothesis is accepted.
The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.
Step-by-step explanation:
Step:-(1)
Given data 28 25 29 25 32 36 27 24
Sample size 'n' = 8
mean of the sample (x⁻) = ∑x /n = [tex]\frac{28+ 25+ 29 +25 +32 +36 + 27 + 24}{8}[/tex]
mean of the sample (x⁻) = 28.25
x x- x⁻ (x-x⁻ )²
28 28 - 28.25 = -0.25 0.0625
25 25 -28.25 = -3.25 10.56
29 29-28.25 = 0.75 0.5625
25 25-28.25 = -3.25 10.56
32 32-28.25 = 3.75 14.06
36 36-28.25 = 7.75 60.06
27 27-28.25 = -1.25 1.5625
24 24-28.25 = -4.25 18.06
∑(x-x⁻)² = 115.4875
Step:-(2)
The sample standard deviation
S² = ∑(x-x⁻)²/n-1 = [tex]\frac{115.4875 }{7}[/tex] = 16.49
By using χ² distribution
χ² = [tex]\frac{ns^2 }{variance}[/tex]
By above test can be applied only if the population from which sample is drawn normal.
Given data For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.
Population variance σ² = 23
Step:-(3)
Null hypothesis :H₀:σ² = 23
Alternative hypothesis :H₁:≠23
[tex]X^{2} = \frac{8 (16.49)}{23}=5.7356[/tex]
The calculated chi -square value =5.7356
The degrees of freedom γ=n-1 =8-1=7
The tabulated value of chi -square = 12.01 at 0.1level of significance (check table)
The calculated chi -square value =5.7356 Is less than12.01 at 0.1level of significance .
The null hypothesis is accepted.
Conclusion:-
The null hypothesis is accepted.
The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.
Related Questions
A review of 200 days-away-from-work injuries for a large, multi-facility corporation was conducted, and it was determined that 18 of them were due to lower back injuries. Only 14.3 were expected under normal conditions. The rest of the injuries were due to other causes where 185.7 were expected. What is the chi-square value? Discuss whether there was a significant difference in observed data vs. the expected data. Also, discuss how the process of hypothesis testing might prove helpful to the safety professional.
Answers
Answer:
a) Chi square value = 1.031
b) There is no significant difference between the observed and expected values.
c) Check explanations for the part C of the question
Step-by-step explanation:
a) People away from work due to lower back injuries:
Observed value = 18
Expected value = 14.3
People away from work due to other injuries:
Observed value = 200 - 18 = 182
Expected value = 185.7
The chi square value is calculated by the formula:
[tex]x^{2} = \frac{(O-E)^{2} }{E}[/tex]
For people out of work due to lower back injuries:
Chi square value,
[tex]x^{2} = \frac{(18-14.3)^{2} }{14.3} \\x^{2} = 0.957[/tex]
For people out of work due to other injuries:
Chi square value,
[tex]x^{2} = \frac{(182-185.7)^{2} }{185.7} \\x^{2} = 0.074[/tex]
Total chi square value for the distribution:
[tex]x^{2} = 0.074 + 0.957\\x^{2} = 1.031[/tex]
b) The degree of freedom, df = n -1
n = 2 ( two categories of people are considered)
df = 2-1 = 1
For df = 1 and, chi square = 1.031
P - value = 0.3099
p- value = 0.3099, the result is not significant at p < 0.05
There is no significant difference between the observed and expected values.
c) Hypothesis testing helps the safety professionals to statistically analyse any situations and determine whether or not they are safe. It can help them to predict the outcome of a given situation by making necessary observations.
I get HOW to make a box and whisker plot. What I don't get is WHY you would want to make one. From a practical point of view, what can it teach you?
Answers
Answer:
I'd say go to Wikipedia and look it up. It is something that cannot be summarized into just a few words.
Step-by-step explanation:
Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform LetUse Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) WebAssign Plotf be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = cos(t), 0 ≤ t < π 0, t ≥ π
Answers
Answer:
[tex]F(s) = \frac{s(e^{\pi s}+1)}{s^2 +1}[/tex]
Step-by-step explanation:
Using the formula for Laplace the transformations if [tex]F(s)[/tex] is the converted function then
[tex]F(s) = \int\limits_{0}^{\infty} e^{-st} \cos(t) dt = \int\limits_{0}^{\pi} e^{-st} \cos(t) dt[/tex]
To solve that integral you need to use integration by parts, when you do integration by parts you get that
[tex]F(s) = \frac{s(e^{\pi s}+1)}{s^2 +1}[/tex].
Answer:
The laplace transform is [tex] F(s) = \frac{s(1+e^{-s\pi})}{s^2+1}[/tex]
Step-by-step explanation:
Let us asume that f(t) =0 for t<0. So, by definition, the laplace transform is given by:
[tex]I = \int_{0}^\pi e^{-st}\cos(t) dt[/tex]
To solve this integral, we will use integration by parts. Let u= cos(t) and dv = [tex]e^{-st}[/tex], so v=[tex]\frac{-e^{st}}{s}[/tex] and du = -sin(t), then, in one step of the integration we have that
[tex]I = \left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi- \int_{0}^\pi \frac{\sin(t) e^{-st}}{s} dt[/tex]
Let [tex] I_2 = \int_{0}^\pi \frac{\sin(t) e^{-st}}{s} dt[/tex]. We will integrate I_2 again by parts. Choose u = sin(t) and dv = [tex]\frac{e^{-st}}{s}[/tex]. So
[tex] I_2 = \left.\frac{-\sin(t) e^{-st}}{s^2}\right|_{0}^\pi + \int_{0}^\pi \frac{\cos(t) e^{-st}}{s^2}dt [/tex]
Therefore,
[tex]I = \left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi - (\left.\frac{-\sin(t) e^{-st}}{s^2}\right|_{0}^\pi - \frac{1}{s^2} I[/tex]
which is an equation for the variabl I. Solving for I we have that
[tex]I(\frac{s^2+1}{s^2}) =\left.\frac{-\cos(t) e^{-st}}{s}\right|_{0}^\pi+\left.\frac{\sin(t) e^{-st}}{s^2}\right|_{0}^\pi[/tex]
Then,
[tex]I = \left.\frac{-s\cos(t) e^{-st}}{s^2+1}\right|_{0}^\pi+\left.\frac{\sin(t) e^{-st}}{s^2+1}\right|_{0}^\pi[/tex].
Note that since the sine function is 0 at 0 and pi, we must only care on the first term. Then
[tex]I = \left.\frac{-s\cos(t) e^{-st}}{s^2+1}\right|_{0}^\pi = \frac{s}{s^2+1}(1-(-1)e^{-s\pi}} = \frac{s(1+e^{-s\pi})}{s^2+1}[/tex]
Hi I need help with this, I am very confused
Answers
Answer:
1/81
Step-by-step explanation:
P(1st ticket is a winner) = 1/9
These are independent events
P(2nd ticket is a winner) = 1/9
P (winner, winner) = 1/9 * 1/9 = 1/81
Suppose you toss a coin 100
times and get 67
heads and 33
tails. Based on these results, what is the probability that the next flip results in a tail
?
Answers
The probability of getting a tail on the next coin flip remains at 50 percent, regardless of the previous series of outcomes because each coin flip is an independent event.
Explanation:The question is concerned with the probability of getting a tail after having tossed a coin 100 times and obtaining 67 heads and 33 tails. Despite the past results of these tosses, the coin still has a 50 percent chance of landing on heads or tails on any given flip. This concept is based on the idea that each coin flip is an independent event with its own probability, unaffected by previous outcomes.
To answer the student's question directly, the probability that the next flip results in a tail is still 50 percent because past results do not change the probability of future coin flips. This is supported by the law of large numbers, which states that as the number of trials increases, the relative frequency of results will get closer to the expected probability.
3/4(1440) + 295.25 + (-33.50)
Answers
Answer:
Your answer is 1341.75
Step-by-step explanation:
3/4 x 1440 = 1080
1080 + 295.25 = 1375.25
1375.25 + -33.50 = 1341.75
The solution of the given expression 3/4(1440) + 295.25 + (-33.50) involving multiplication, addition, and subtraction in mathematics is equal to 1341.75.
The expression provided is:
3/4(1440) + 295.25 + (-33.50)
To solve this, we need to follow the order of operations (PEMDAS):
Multiply 3/4 by 1440 to get 1080.
Add 1080 to 295.25 to get 1375.25.
Finally, subtract 33.50 from 1375.25 to get the final answer of 1341.75.
Find the percentage of people in the sample who prefer blue.
Answers
There is no sample given, please provide us with an attachment for your answer.
Which expression is equivalent to:
16(w+q)
A. (m + 16) (w + 16) B.16w + 169
C. 16w +9
D. W + 169
Answers
The equivalent expression to 16(w+q) is 16w + 16q, but none of the given options A, B, C, or D are correct as they do not accurately represent this distribution. The closest option would be C (16w + 9), though it is still incorrect because it has 9 instead of 16q.
Explanation:The question asks which expression is equivalent to 16(w+q). The correct way to distribute a constant over a sum inside parentheses is to multiply each term inside the parentheses by that constant. So, 16 must be multiplied by both w and q.
Therefore, the equivalent expression is 16w + 16q. Looking at the provided options:
A. (m + 16) (w + 16) includes additional terms and multiplication not present in the original expression.B. 16w + 169 includes the term 169, which is not correct since no such number results from multiplying 16 by q.C. 16w + 16q is correct, but as given in the option just as 16w + 9 it is incorrect because it has 9 instead of 16q.D. w + 169 does not multiply w by 16 and includes the incorrect number 169.Since none of the given options are exactly 16w + 16q, no available option is a correct equivalent expression to 16(w+q).
Suppose that f (400 )equals3000 and f prime (400 )equals10. Estimate each of the following. (a) f (401 )(b) f (400.5 )(c) f (399 )(d) f (398 )(e) f (399.75 )
Answers
Answer:
a) [tex]f(401) = 3010[/tex], b) [tex]f(400.5) = 3005[/tex], c) [tex]f(399) = 2990[/tex], d) [tex]f(398) = 2980[/tex], e) [tex]f(399.75) = 2997.5[/tex]
Step-by-step explanation:
The estimation of each value can be found by the following value:
[tex]f(x + \Delta x) = f(x) + f'(x)\cdot \Delta x[/tex]
a) [tex]f(401) = 3000 + 10\cdot (401-400)[/tex]
[tex]f(401) = 3010[/tex]
b) [tex]f(400.5) = 3000 + 10\cdot (400.5 - 400)[/tex]
[tex]f(400.5) = 3005[/tex]
c) [tex]f(399) = 3000 + 10\cdot (399 - 400)[/tex]
[tex]f(399) = 2990[/tex]
d) [tex]f(398) = 3000 + 10\cdot (398-400)[/tex]
[tex]f(398) = 2980[/tex]
e) [tex]f(399.75) = 3000 + 10\cdot (399.75-400)[/tex]
[tex]f(399.75) = 2997.5[/tex]
Someone please help, this is my last resort
Answers
Answer:
34 5/8
Step-by-step explanation:
you just add all the numbers on the left and the two drawer numbers then boom!!
Kings Department Store has 625 rubies, 800 diamonds, and 700 emeralds from which they will make bracelets and necklaces that they have advertised in their Christmas brochure. Each of the rubies is approximately the same size and shape as the diamonds and the emeralds. Kings will sell each bracelet for $400 and it costs them $150 to make it. Each bracelet is made with 2 rubies, 3 diamonds, and 4 emeralds. Kings will sell each necklace for $700 and it costs them $200 to make it. Each neckalce is made with 5 rubies, 7 diamonds, and 3 emeralds. a) Formulate the above problem as a Linear Programming problem with the objective of maximizing profit
Answers
Step-by-step explanation:
Let Xb be the no of braclets made
Let Xn be the no of necklaces made
Max Z=250Xb + 500Xn (Objective Function)
Subject to
2Xb + 5Xn <= 625 (rubies)
3Xb + 7 Xn <= 800 ( diamonds)
4Xb + 3 Xn <= 700 (Emeralds)
Xb>=0 (non-negativity)
Xn >= 0 (non negativity
Answer:
Step-by-step explanation:
We are to Formulate the question given as a Linear Programming problem with the objective of maximizing profit.
From the question;
Kings will sell each bracelet for $400 and it costs them $150 to make it.
This implies that; King will net a profit on $250 on each bracelet made with 2 rubies, 3 diamonds, and 4 emeralds :
Also;
Kings will sell each necklace for $700 and it costs them $200 to make it
i.e King will net a profit of $500 on each necklace made with 5 rubies, 7 diamonds, and 3 emeralds.
Now; let's assume that :
[tex]Y_{br}[/tex] be the no of bracelets made ; &
[tex]Y_{nk}[/tex] be the no of necklaces made
[tex]\\ \\Max \ Z=250 \ Y{_b_r}} + 500 \ Y{_n_k}[/tex] (Objective Function)
Subject to :
[tex]2 \ Y_{br} + 5 \ Y_{nk}[/tex] ← 625 (rubies)
[tex]3 \ Y_{br} + 7 \ Y_{nk}[/tex] ← 800 ( diamonds)
[tex]4 \ Y_{br} + 3 \ Y_{nk}[/tex] ← 700 (Emeralds)
[tex]\\ \\Y_{br} \\[/tex] ⇒ 0 (non-negativity)
[tex]\\\\ \ Y_{nk}\\[/tex] ⇒ 0 (non negativity)
A student wants to compare textbook prices for two online bookstores. She takes a random sample of five textbook titles from a list provided by her college bookstore, and then she determines the prices of those textbooks at each of the two websites. The prices of the five textbooks selected are listed below in the same order for each online bookstore. A: $115, $43, $99, $80, $119 B: $110, $40, $99, $69, $109 (a) Are these independent or dependent samples
Answers
Answer:
Dependent sample: The same textbook are being compared.
Step-by-step explanation:
We are given the following in the question:
A student wants to compare textbook prices for two online bookstores.
Sample 1 from bookstore A:
$115, $43, $99, $80, $119
Sample 2 from bookstore B:
$110, $40, $99, $69, $109
Dependent and independent sample:
Dependent samples are paired observations for same set of items.Independent samples are observations made on two different sets of items.If the values in one sample affect the observations in the other sample, then the samples are dependent.If the values in one sample have no effect about those of the other sample, then the samples are independent.Thus, the given sample is dependent sample as the same textbook is being compared from two different bookstore.
The textbook prices listed for the two different online bookstores are dependent samples, as the prices are paired for the same textbooks across the two bookstores. Analyzing this data would involve using statistical methods suitable for dependent samples, like paired t-tests.
Explanation:The textbook prices listed by the student for the two different online bookstores represent dependent samples. This is because the prices are paired for the same textbooks across the two bookstores. They are not independent samples because the price of a given book in one store could potentially influence the price of the same book in the other store. For example, if one store lowers its prices, the other might follow suit to remain competitive.
Consideration of such data requires the analysis method suitable for dependent samples. Specifically, using methodologies like paired t-tests in statistics might be appropriate in this scenario to compare the prices from the different online bookstores. These methods account for the fact that measurements within each pair could be correlated.
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Your boss tells you that she knows the length of the widgets your company makes is normally distributed with a mean of 25 inches and a population standard deviation of 12 inches. If you take samples of size 9 from finished widgets in the warehouse, in order to check for quality, what will be the mean and standard deviation of the sampling distribution?
Answers
Answer:
Mean of sampling distribution = 25 inches
Standard deviation of sampling distribution = 4 inches
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 25 inches
Standard Deviation, σ = 12 inches
Sample size, n = 9
We are given that the distribution of length of the widgets is a bell shaped distribution that is a normal distribution.
a) Mean of the sampling distribution
The best approximator for the mean of the sampling distribution is the population mean itself.
Thus, we can write:
[tex]\bar{x} = \mu = 25\text{ inches}[/tex]
b) Standard deviation of the sampling distribution
[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{12}{\sqrt{9}} = 4\text{ inches}[/tex]
Using the Central Limit Theorem, it is found that:
The mean of the distribution would be of 25 inches.The standard deviation of the distribution would be of 4 inches.The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For the population:
Mean of 25 inches, thus [tex]\mu = 25[/tex]Standard deviation of 12 inches, thus [tex]\sigma = 12[/tex].Samples of size 9, thus [tex]n = 9[/tex].
By the Central Limit Theorem:
The mean of the sampling distribution is [tex]\mu = 25[/tex].The standard deviation of the sampling distribution is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{12}{\sqrt{9}} = 4[/tex].A similar problem is given at https://brainly.com/question/15519778
Which events have a probability of 25 percent? Select three options.
choosing a green jelly bean out of a bag that contains 2 green jelly beans, 1 red jelly bean, and 5 yellow jelly beans
rolling a number less than 3 on a six-sided die
spinning a number less than 2 on a spinner that has four equal sections numbered from 1 to 4
choosing an Oregon state quarter out a bag that contains 4 California state quarters, 3 Oregon state quarters, 6 Texas state quarters, and 3 New York state quarters
choosing a spade out of a standard deck of cards that contains 13 hearts, 13 clubs, 13 diamonds, and 13 spades
Answers
Choosing a green jelly bean.
Spinning a number less than 2 on a spinner.
Choosing a spade out of a standard deck of cards.
What are the probabilities?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of choosing a green jelly bean = number of green jelly bean / total number of beans
2/8 x 100 = 25%
Probability of spinning a number less than 2 on a spinner = number that is less than 2 / total number of sections
1/4 x 100 = 25%
Probability of choosing a choosing a spade= number of spade / total cards in the deck
13/54 x 100 = 25%
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The three options that have a probability of 25 percent are:
- Choosing a green jelly bean
- Spinning a number less than 2 on a spinner
- Choosing a spade from a standard deck of cards
The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. A probability of 25 percent corresponds to a ratio of 1 out of 4 (since 25% is one-fourth of 100%). Let's analyze the options:
1. Choosing a green jelly bean: There are 2 green jelly beans out of a total of 2 + 1 + 5 = 8 jelly beans. The probability is 2/8, which simplifies to 1/4 or 25%. This option has a probability of 25%.
2. Rolling a number less than 3 on a six-sided die: There are 2 favorable outcomes (1 and 2) out of 6 possible outcomes (1 through 6). The probability is 2/6, which simplifies to 1/3 or approximately 33.33%. This option does not have a probability of 25%.
3. Spinning a number less than 2 on a spinner: There is 1 favorable outcome (1) out of 4 possible outcomes (1 through 4). The probability is 1/4 or 25%. This option has a probability of 25%.
4. Choosing an Oregon state quarter: There are 3 Oregon state quarters out of a total of 4 + 3 + 6 + 3 = 16 state quarters. The probability is 3/16, which is not equal to 25%.
5. Choosing a spade from a standard deck of cards: There are 13 spades out of a total of 13 + 13 + 13 + 13 = 52 cards. The probability is 13/52, which simplifies to 1/4 or 25%. This option has a probability of 25%.
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The distance from Parrot Point Airport to the Ivy Cliffs is 172 miles at and angle of 7.0 degrees northeast. There is a wind blowing southeast at 25 miles per hour. You want to make this trip in 2 hours by flying straight there. At what speed* and heading should you fly?
Answers
Answer:
Speed = x/t = 146.61/2 = 73.30 mph
direction y = 22.59° northeast
Step-by-step explanation:
Given;
The distance from Parrot Point Airport to the Ivy Cliffs is 172 miles at and angle of 7.0 degrees northeast;
Resultant distance R = 172 (7° northeast)
Time given to make the trip t = 2 hours
Distance moved by wind during the time dw = 25×2 = 50 miles south east.
Let x represent the distance covered by plane without wind during the time and y the direction;
Resolving into horizontal and vertical component;
horizontal;
x cosy + 50cos45 = 172cos7
xcosy = 172cos7 - 50cos45 .....1
Vertical;
xsiny - 50sin45 = 172sin7
xsiny = 172sin7 + 50sin45 .....2
Divide equation 2 by 1
xsiny/xcosy = (172sin7 + 50sin45)/(172cos7 - 50cos45)
tany = 0.4160
y = taninverse (0.4160)
y = 22.59° northeast
Substituting y into equation 2;
xsin22.59 = 172sin7 + 50sin45
x = (172sin7 + 50sin45)/sin22.59
x = 146.61 miles
Speed = x/t = 146.61/2 = 73.30 miles per hour
Speed = 73.30mph
If probability of catching a cold is 0.03, what is the probability of 3 people out of six catching a cold?
Answers
Answer:
[tex]P(X=x)=0.0004928[/tex]
Step-by-step explanation:
-This is a binomial probability problem.
-Given the probability of catching a cold is 0.03, n=6
#The probability of exactly 3 people catching a cold is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X=3)={6\choose3}0.03^3(1-0.03)^3\\\\=0.0004928[/tex]
Hence, the probability of exactly 3 in 6 people catching a cold is 0.0004928
Lonnie has a shutter that is 4 yards, 17 inches long. How many inches long is Lonnie's shutter?
Answers
Answer:
161 inches
Step-by-step explanation:
This problem is all about conversion. How many feet are in a yard? 3. How many feet are in 4 yards? 12 feet. There are 12 inches in a foot. 12 feet means 12 x 12 inches, which is 144. 144 + the other 17 inches, is 161.
Answer:
The answer is into the unkown
Step-by-step explanation:
elsa and anna are good sisters olaf olaf anna fiftys ahdpnf3oehisklNHW3q3tsqagwgdraw4gw
A half-century ago, the mean height of women in a particular country in their 20s was 64.7 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.07 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 21 of today's women in their 20s have mean heights of at least 65.86 inches?
Answers
Answer:
99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.
Step-by-step explanation:
We are given that a half-century ago, the mean height of women in a particular country in their 20's was 64.7 inches. Assume that the heights of today's women in their 20's are approximately normally distributed with a standard deviation of 2.07 inches.
Also, a samples of 21 of today's women in their 20's have been taken.
Let [tex]\bar X[/tex] = sample mean heights
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean height of women = 64.7 inches
[tex]\sigma[/tex] = standard deviation = 2.07 inches
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the sample of 21 of today's women in their 20's have mean heights of at least 65.86 inches is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 65.86 inches)
P([tex]\bar X[/tex] [tex]\geq[/tex] 65.86 inches) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{65.86-64.7}{\frac{2.07}{\sqrt{21} } }[/tex] ) = P(Z [tex]\geq[/tex] -2.57) = P(Z [tex]\leq[/tex] 2.57)
= 0.99492 or 99.5%
The above probability is calculated by looking at the value of x = 2.57 in the z table which has an area of 0.99492.
Therefore, 99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.
In 10-mph crash tests, 25% of a certain type of automobile sustain no visible damage. A modified bumper design has been proposed in an effort to increase this percentage. Let denote the proportion of all cars with this new bumper that sustain no visible damage in 10-mph crash test. The hypothesis to be tested is The test will be based on an experiment involving independent crashes of car prototypes with the new bumper. Let denote the number of crashes resulting in no visible damage, and consider the test procedure that rejects
(a) Find the probability of type I error.
Answers
Answer:
(a) Find the probability of type I error. = 0.1018
Step-by-step explanation:
check attachment for the answer
Answer:
The probability of Type I error is = 0.10185.
Step-by-step explanation:
Solution:-
The type I - error is defined as the probability of rejecting Null hypothesis defined by Alternate hypothesis:
Ha : X ≥ 8
Where,
X : Denote the number of cars crash with no visible damage
The random variate "X" is defined by binomial distribution:
X ~ B ( n = 20 , p = 0.25 )
- The probability of Type I error:
P (Type I error ) = P ( Reject Null hypothesis )
= P ( X ≥ 8 )
- The probability mass function of binomial random variate "X" is given:
[tex]P ( X = x ) = nCr (p)^r * (1-p)^(^n^-^r^)\\P ( X \geq 8 ) = 1 - P ( X < 8 )\\\\P ( X \geq 8 ) = 1 - [ P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) + P ( X = 6 ) + P ( X = 7 ) ][/tex][tex]P ( X \geq 8 ) = 1 - [ (0.75)^2^0 + 20(0.25)*(0.75)^1^9 + 20C2(0.25)^2*(0.75)^1^8 +\\\\ 20C3(0.25)^3*(0.75)^1^7 + 20C4(0.25)^4*(0.75)^1^6 + 20C5(0.25)^5*(0.75)^1^5\\\\ + 20C6(0.25)^6*(0.75)^1^4 + 20C7(0.25)^7*(0.75)^1^3 ] \\\\\\P ( X \geq 8 ) = 1 - [ 0.00317 + 0.02114 + 0.06694 + 0.13389 + 0.18968 + 0.20233\\\\+ 0.16860 + 0.11240]\\\\P ( X \geq 8 ) = 1 - 0.89815 = 0.10185[/tex]
Answer: The probability of Type I error is = 0.10185.
Amara needs 454545 kilograms of meat to feed her 222 pet dragons each day. Each pet dragon eats the same amount of meat.
Answers
Answer:
2047.5 kg
Step-by-step explanation:
There's a total of 454545 kg of meat, and each dragon gets x kg. There are 222 dragons. So, we have the equation: 222x = 454545
Divide by 222 from both sides: x = 2047.5 kg
Thus, each dragon gets 2047.5 kg of meat.
Hope this helps!
Write the word sentence as an equation. Then solve the equation.
10 more than a number c is 3
Answers
Answer:
Equation: 10+c=3
Answer: c=-7
Step-by-step explanation:
1. 10+c=3
2. c=3-10
3. c=-7
Answer:
c=-7
Step-by-step explanation:
c+10=3
Subtract 10 from both sides
c=-7
It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each night, on average. The researcher randomly sampled 20 college students and calculated a sample mean of 7.5 hours per night. If the researcher wanted to perform a one-sample t-test, which of the following is a correct statement?
A: By taking a random sample, the researcher has guaranteed that the distribution of number of hours of sleep per night for all college students is normal.
B.The number of hours of sleep per night for all college students must be normally distributed because the sample size is small.
C.By taking a random sample, the researcher has guaranteed that the distribution of sample means is normal.
D.The distribution of sample means will be normal even if the distribution of the data in the population is not normal.
Answers
In a one-sample t-test, the normal distribution of sample means is more important than the normality of individual data in the population. This follows the Central Limit Theorem which states that, with a decently large sample size, the distribution of sample means will approach normality regardless of the population distribution.
Explanation:Statement C is the correct option. The Central Limit Theorem indicates that regardless of the population distribution, as long as we have a sufficiently large sample size, the sample means will be approximately normally distributed. However, this doesn't guarantee that the distribution of the individual data (the number of sleep hours) in the population is normal.
It’s important to note two things: First, the idea of random sampling is to avoid bias and to have a representative sample of the population under study. Second, the rule of thumb is that the sample size should be approximately 30 or greater for the Central Limit Theorem to take effect, to provide a decent approximation of a normal distribution of sample means. In this instance, a sample size of 20 is close to 30, so we may anticipate that the sample mean distribution is roughly normal.
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select each angle that has a measure of 30
Answers
Answer:
Please post another question with the angle that you were given. Thank you!
Step-by-step explanation:
There wasn't any angles given therefore, I couldn't help!
Can someone explain this please???
Answers
A function is a rule that assigns exactly one output to a given input. The input is taken from a set called the domain, and the corresponding output belongs to a set called the range.
1. In this exercise, we're calling the pool of patients 1-8 the domain, and the pool of nurses A-D the range. The given table describes a function because any patient is assigned to only one nurse.
2. This wouldn't be a function if at least one patient was assigned to more than one nurse. If this were to happen in practice, the patient could be, say, given the same dose of some medicine twice if the nurses aren't careful.
3. Making the nurse pool the domain and the patient pool the range would give a relation that is not a function, since more than one patient is assigned to one nurse.
There was a trucking strike that caused a prime ingredient in your menu item to shoot up 17%. You were paying $12 per package. How much will you have to increase the price of the menu item if you wish to maintain your current dollar profit margin on the menu item? a) $2.04 b) $6.37 c) $7.15 d) $9.44
Answers
The amount by which we must raise the price in order to retain your existing dollar profit margin is $2.04; the right solution is (a).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
There was a trucking strike that caused a prime ingredient in your menu item to shoot up by 17%. You were paying $12 per package.
The increases in the price of the ingredient = 17% of 12
Increase = 0.17 × 12
Increase = 2.04
Therefore, the amount by which we must raise the price in order to retain your existing dollar profit margin is $2.04; the right solution is (a).
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The price of the menu item should be increased by $2.04.
Let's begin by calculating the new cost per package after the price increase. If the original cost per package was $12 and it increased by 17%, we calculate the increase as follows:
Increase = 12 * 0.17 = 2.04
The new cost per package will be:
New cost = 12 + 2.04 = 14.04
To maintain the same dollar profit margin on your menu item, you need to increase the price by the same amount as the cost increase, which is $2.04.
Please help me, Please I will give you 15 points and brainliest
The King Cobra is a roller coaster. It sells more than 900 tickets each day. What inequality can you write to show the ticket sales, t? How would you graph the solutions of the inequality?
Answers
Answer: The inequality could be t > 900. Draw a number line so it includes 900. Draw an open circle on 900. Shade all the numbers greater than 900, or to the right.
Step-by-step explanation:
Inequality- Inequality is the something that is equal to the something or less than that of the sign give the conditions on which the graph is drawn on the basis of sales occured profits occured
It is the dotted line drawn if the curve is increasing or decreasing then the sign comes <,> It is the solid line occurs drawn if the sales occur according to the profit occurs constantly or equal to the at least value [tex]\leq \geq[/tex] sign indicatesExplanation to the above is the that mentioned below:
The graph of inequality makes the solid line. Due to the roller coaster king cobra the ticket sales more than 900 each day and its constantly increasing day by day It providing smooth curve on the daily basis due to the sell of tickets more with constant rate.Thus we conclude that from the above the graph of the equation is solid line.
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At the end of the current year, Accounts Receivable has a balance of $4,375,000; Allowance for Doubtful Accounts has a debit balance of $21,300; and sales for the year total $102,480,000. Using the aging method, the balance of Allowance for Doubtful Accounts is estimated as $205,000.
a. Determine the amount of the adjusting entry for uncollectible accounts.
Answers
Answer:
$226,300
Step-by-step explanation:
Given Allowance for Doubtful Accounts is estimated as $205,000 and Allowance for Doubtful Accounts has a debit balance of $21,300
#The amount of the adjusting entry for uncollectible accounts is calculated as below:
[tex]Adjustment \ Cost=Allowance\ Doubtful\ Accounts +Doubtful \ Accounts \ Debit \ Balance\\\\=205000+21300\\\\\$226,300[/tex]
Hence, the amount of the adjusting entry for uncollectible accounts is $226,300
Jimmy is a flag person and earned $321.10 last week for 32.5 hours work. What is his hourly wage? *
Your answer
Answers
What is inequality for 48-15=
Answers
Answer:
48-15 is 33
Step-by-step explanation:
Kim wants to buy a car. Help Kim compute the monthly payment on a loan, given the loan amount, the annual percentage rate of interest, and the number of monthly payments.The program should allow Kim to input the loan amount, interest rate, and how many payments she wants to make.It should then compute and display the monthly payment.You will need the following variables:Payment LoanAmt InterestRateMonthlyRate NumberMonthsYou will need the following formulas:MonthlyRate = InterestRate/1200Note: when the user enters InterestRate as a percentage, it must be divided by 100 to make it a decimal (i.e., 18% = 18/100 = 0.18).The InterestRate offered by car dealers is an annual rate so this must be divided by 12 to get the MonthlyRate.The formula given above combines the two steps (i.e., annual rate of 18% = 18/100 = 0.18 and the monthly rate is 0.18/12 = 0.015 or 18/(100*12) = 18/1200.Payment = LoanAmt * MonthlyRate * (1 +MonthlyRate)^NumberMonths (divided by) ((1 +MonthlyRate)^NumberMonths -1)Note: The formula must be entered carefully, exactly as shown.
Answers
Answer:
The complete Python program to calculate the monthly payment on a loan with step by step explanation is given below.
Python Code with Explanation:
# get the loan amount from the user
LoanAmt=eval(input("Please enter the loan amount: "))
# get the annual interest rate from the user in percentage form
InterestRate=eval(input("Please enter the annual interest rate in percentage: "))
# get the number of months from the user
NumberMonths=eval(input("Please enter the number of months: "))
# convert the annual interest rate into monthly interest rate and also into decimal form according to the equation given in the question
MonthlyRate = InterestRate/1200
# implement the given equation to find out the required monthly payment, the operator (**) is used to raise to the power
Payment = (LoanAmt*MonthlyRate (1+MonthlyRate)**NumberMonths)/((1+MonthlyRate)**NumberMonths -1)
# finally, print the monthly payment
print("The monthly payment is: ", Payment)
Output:
Please enter the loan amount: 1500
Please enter the annual interest rate in percentage: 15
Please enter the number of months: 12
The monthly payment is: 135.38746851773584
Bonus:
You can use this command to limit the digits after the decimal point
For example following code will limit to 2 digits after the decimal point.
print(format(Payment, '.2f'))