Answer:
24 324
Step-by-step explanation:
21334 fda adf
Answer: 24, 324
Step-by-step explanation:
Find the perimiter of both sides
Consider the following system of equations. StartLayout Enlarged left-brace 1st row y = 6 x squared 2nd row y = x squared + 4 EndLayout Which statement describes why the system has two solutions? Each graph has one y-intercept, which is a solution. Each graph has one vertex, which is a solution. The graphs of the equations intersect the x-axis at two places. The graphs of the equations intersect each other at two places.
Answer:
The graphs of the equations intersect each other at two places.
The correct answer is the graphs of the equations intersect each other at two places.
Why does an equation have 2 solutions?A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solutions.
How do you know if a graph has two solutions?Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
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The amount of soda in a 16-ounce can is normally distributed with a mean of 16 ounces and a standard deviation of .5 ounce. What is the probability that a randomly selected can will have less than 15.5 ounces? Round your answers to four decimal places.
Under a normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounce, there's a 15.87% probability that a randomly selected can will have less than 15.5 ounces of soda.
Explanation:This question is related to probability within the field of statistics. Particularly, it's about the normal distribution, a common statistical distribution that shows the spread of data around the mean. In this specific case, the amount of soda in a 16-ounce can is normally distributed with a mean (µ) of 16 ounces and a standard deviation (σ) of 0.5 ounce.
We're asked to calculate the probability that a randomly selected can will have less than 15.5 ounces. This requires us to standardize the score of 15.5, meaning we use the formula (X - µ) / σ, where X is the value we are assessing. So, (15.5 - 16) / 0.5 equals -1.
This standardized score is known as a z-score, and tells us how many standard deviations a value is from the mean. In this case, 15.5 is one standard deviation below the mean. We then look up this z-score in a z-table, which gives us the probability associated with this z-score. For a z-score of -1, the probability is 0.1587, or 15.87%.
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The probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.
To find the probability that a randomly selected can will have less than 15.5 ounces, we can use the standard normal distribution.
First, we need to calculate the z-score for 15.5 ounces using the formula:
[tex]\[ z = \frac{{X - \mu}}{{\sigma}} \][/tex]where:
X is the value we're interested in (15.5 ounces), [tex]\( \mu \)[/tex]is the mean (16 ounces), [tex]\( \sigma \)[/tex] is the standard deviation (0.5 ounce).Plugging in the values:
[tex]\[ z = {{15.5 - 16}}/{{0.5}} \][/tex][tex]\[ z = {{-0.5}}/{{0.5}} \][/tex]z = -1Next, we look up the z-score of -1 in the standard normal distribution table to find the probability. The probability that a randomly selected can will have less than 15.5 ounces is the area to the left of the z-score of -1.
Using the standard normal distribution table, the area to the left of -1 is approximately 0.1587.
Therefore, the probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.
The Martin family's truck gets an average of 35 miles per gallon. Predict how many miles they can drive
using 4 gallons of gas.
Answer:
25 miles per gallon x 7 gallons used=175 miles driven
175/7=25
NOTE: THIS IS AN EXAMPLE
An angle measures 30° more than the measure of its complementary angle. What is the measure of each angle?
Angle: [tex]\( 60^\circ \)[/tex], complementary angle: [tex]\( 30^\circ \)[/tex]. Angle is 30° more than its complementary angle.
Let's denote the measure of the angle as [tex]\( x \)[/tex] degrees.
The complementary angle would be [tex]\( 90^\circ - x \)[/tex] degrees.
Given that the angle measures 30° more than its complementary angle, we can write the equation:
[tex]\[ x = (90^\circ - x) + 30^\circ \][/tex]
Now, let's solve for [tex]\( x \)[/tex]:
[tex]\[ x = 90^\circ - x + 30^\circ \][/tex]
[tex]\[ 2x = 90^\circ + 30^\circ \][/tex]
[tex]\[ 2x = 120^\circ \][/tex]
Dividing both sides by 2:
[tex]\[ x = \frac{120^\circ}{2} \][/tex]
[tex]\[ x = 60^\circ \][/tex]
So, the angle measures [tex]\( 60^\circ \)[/tex] and its complementary angle measures:
[tex]\[ 90^\circ - 60^\circ = 30^\circ \][/tex]
Therefore, the measure of the angle is [tex]\( 60^\circ \)[/tex] and the measure of its complementary angle is [tex]\( 30^\circ \)[/tex].
The Eastside High School marching band is made up of the instrument players and the percussion. If there are 245 members who play instruments and 35 percussion members, then what percent of the marching band is percussion?
Answer:
14%
Step-by-step explanation:
you divide 35 by 245 to get 0.14285714285 than you round
It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. A random sample of 25 customers is selected. Assume that the customers’ purchases are made independently. In this binomial distribution application, which Excel statement will find the probability of between 5 and 10 customers, inclusively, purchasing a pair of running shoes?
Answer:
=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)
0.001324586
Step-by-step explanation:
The success probability is p = 70% = 0.70
The number of trials are n = 25
The Excel formula for the binomial distribution is given by
BINOMDIST(Number_s, Trial_s, Probability_s, Cumulative)
Where
Numbers = 5 and 10
Trials = 25
Probability = 70%
Cumulative = FALSE
The probability of between 5 and 10 customers is then
=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)
0.001324586
Note: FALSE option provides the probability of exactly 10 and 5 where TRUE option gives cumulative results (0 to 5 or 0 to 10) that would be wrong in this case.
Using the binomial distribution, it is found that the Excel statement that will find the probability of between 5 and 10 customers is:
BINON.DIST.RANGE(25, 0.75, 5, 10)
For each customer, there are only two possible outcomes, either they purchase a pair of running shoes, or they do not. Customers' purchases are independent, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.Using Excel, the probability of the number of successes being between a and b, inclusive, is given by:
BINOM.DIST.RANGE(n, p, a, b)
In this problem:
70% of the customers in a sporting goods store purchase a pair of running shoes, hence [tex]p = 0.7[/tex]A random sample of 25 customers is selected, hence [tex]n = 25[/tex].Between 5 and 10 customers, hence [tex]a = 5, b = 10[/tex].Then, the Excel statement is:
BINON.DIST.RANGE(25, 0.75, 5, 10)
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The Big River Casino is advertising a new digital lottery-style game called Instant Lotto. The player can win the following monetary prizes with the associated probabilities: 5% probability to win $10 4% probability to win $15 3% probability to win $30 1% probability to win $50 0.1% probability to win the Grand Prize, $1000. (a) Calculate the expected value of the prize for one play of Instant Lotto. (b) As a promotion, a visitor to the casino is given 20 free plays of Instant Lotto. What is the probability that the visitor wins some prize at least twice in the 20 free plays? (c) The number of people who play Instant Lotto each day is approximately normally distributed with a mean of 800 people and a standard deviation of 310 people. What is the probability that a randomly selected day has at least 1000 people play Instant Lotto?
Answer:
(a) The expected value of the prize for one play of Instant Lotto is $3.50.
(b) The probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.
(c) The probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.
Step-by-step explanation:
(a)
The probability distribution of the monetary prizes that can be won at the game called Instant Lotto is:
X P (X = x)
$10 0.05
$15 0.04
$30 0.03
$50 0.01
$1000 0.001
$0 0.869
___________
Total = 1.000
Compute the expected value of the prize for one play of Instant Lotto as follows:
[tex]E(X)=\sum x\cdot P (X=x)[/tex]
[tex]=(10\times 0.05)+(15\times 0.04)+(30\times 0.03) \\+ (50\times 0.01)+(1000\times 0.001)+(0\times 0.869)\\=0.5+0.6+0.9+0.5+1+0\\=3.5[/tex]
Thus, the expected value of the prize for one play of Instant Lotto is $3.50.
(b)
Let X = number of times a visitor wins some prize.
A visitor to the casino is given n = 20 free plays of Instant Lotto.
The probability that a visitor wins at any of the 20 free plays is, p = 1/20 = 0.05.
The event of a visitor winning at a random free play is independent of the others.
The random variable X follows Binomial distribution with parameters n = 20 and p = 0.05.
Compute the probability that the visitor wins some prize at least twice in the 20 free plays as follows:
P (X ≥ 2) = 1 - P (X < 2)
= 1 - P (X = 0) - P (X = 1)
[tex]=1-[{20\choose 0}0.05^{0}(1-0.05)^{20-0}]-[{20\choose 1}0.05^{1}(1-0.05)^{20-1}]\\=1-0.3585-0.3774\\=0.2641[/tex]
Thus, the probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.
(c)
Let X = number of people who play Instant Lotto each day.
The random variable X is normally distributed with a mean, μ = 800 people and a standard deviation, μ = 310 people.
Compute the probability that a randomly selected day has at least 1000 people play Instant Lotto as follows:
Apply continuity correction:
P (X ≥ 1000) = P (X > 1000 + 0.50)
= P (X > 1000.50)
[tex]=P(\frac{X-\mu}{\sigma}>\frac{1000.50-800}{310})[/tex]
[tex]=P(Z>0.65)\\=1-P(Z<0.65)\\=1-0.74215\\=0.25785\\\approx0.2579[/tex]
Thus, the probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.
Match the operations with the order in which you should do them when
simplifying an exponential expression.
Answer:
It should go exponents, multiplication and division, then addition and subtraction
Step-by-step explanation:
By using PEMDAS, for order of operations, it's easier to remember which set comes first. (parentheses, exponents, multiplication, division, addition, subtraction)
A production process manufactures electronic components with timing signals whose duration follows a normal distribution. A random sample of 55 components was taken, and the durations of their timing signals were measured.a. The probability is 0.01 that the sample variance is bigger than what percentage of the population variance?
b. The probability is 0.05 that the sample variance is less than what percentage of the population variance?
Answer:
Check the explanation
Step-by-step explanation:
b ) [tex]P(s^2<p\sigma^2)=0.05[/tex]
or , [tex]P\left (\frac{(n-1)s^2}{\sigma^2}<(n-1)p \right )=0.05[/tex]
or , [tex]P\left (\chi^2_5<5p \right )=0.05=P(\chi^2_5< 1.145476 )[/tex]
or , 5p =1.145476
or , [tex]p =\frac{1.145476}{5}= 0.2290952[/tex]
Required percentage = 22.91
How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 41 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 35, s = 18.
Answer:
7
Step-by-step explanation:
67ururiierururf8fucicififfifig
A cell phone weighs about 2.8 times 10 Superscript n pounds. Which value of n is most reasonable? Negative 3 Negative 1 0 1
Answer:
-1
Step-by-step explanation:
The weight of the cell phone is given by:
[tex]W=2.8*10^n[/tex]
The options provided for 'n' are:
a. -3
b. -1
c. 0
d. 1
Applying the possible values:
[tex]W_a=2.8*10^{-3}\\W_a = 0.0028\ pounds\\\\W_b=2.8*10^{-1}\\W_b = 0.28\ pounds\\\\W_c=2.8*10^{0}\\W_c = 2.8\ pounds\\\\W_d=2.8*10^{1}\\W_d = 28\ pounds[/tex]
A cellphone could not possibly weigh as little as 0.0028 or as much as 2.8 or 28 pounds. Therefore, the most reasonable value for n is -1.
Answer:
(B)-1
Step-by-step explanation:
Let us plug in the given values into [tex]2.8X10^n[/tex][tex]2.8X10^{-3}=2.8X 0.001=0.0028\:Pounds\\2.8X10^{-1}=2.8X 0.1=0.28\:Pounds\\2.8X10^{0}=2.8X 1=2.8\:Pounds\\2.8X10^{1}=2.8X 10=28\:Pounds[/tex]
A reasonable value for the weight of a cell phone will be 0.28 Pounds.
Therefore, n=-1
Find the volume of this prism.
Image attached
Answer:
840cm³
Step-by-step explanation:
devide them into 2 shapes.
the shape at the bottoma×b×h
15cm×6cm×8cm=720cm³the shape at the topa×b×h
a: 5 cmb: 6 cmh: 12-8=4 cm5cm×6cm×4cm=120cm³V=720cm³+120cm³=840cm³
Answer:
840 cm^3
Step-by-step explanation:
L x W x H = V
Split the prism into 2 different prisms.
6 is constant throughout the figure, so all we have to do is find the L and H of the two prisms and multiply them by 6.
15 x 8 = 120
The height of the higher prism can be determined by subtracting the bottom height from the total height.
12 - 8 = 4
5 x 4 = 20
Add the two side areas together.
20 + 120 = 140
Multiply by the width, 6.
140 x 6 = 840
At a certain university, 22% of the students fail general chemistry on their first attempt. Professor Brown teacher at this university and believes that the rate of first-time failure in his general chemistry classes is 45%. He samples 86 students from last semester who were first-time enrollees in general chemistry and finds that 19 of them failed his course.
1) State the appropriate null and alternate hypotheses.
2) Compute the P-value.
3) Using a = 0.05, can Professor Brown conclude that the percentage of failures differs from 45%?
Answer:
[tex]a. \ H_o:p=0.45, \ \ \ \ H_a:p\neq 0.45\\\\b.\ \hat p=0.2209\\\\c. \ Yes\ (-4.2706<-1.96)[/tex]
Step-by-step explanation:
a. The professor's claim is that 45% first-timers fail his test. The null hypothesis is therefore stated as:
[tex]H_o:p=0.45[/tex]
-The alternative hypothesis is that more or less people fail the test as opposed to the professor's exact claim, hence:
[tex]H_a:p\neq 0.45[/tex]
b. To compute the P-value we use the z-value for a 95% confidence level:
[tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]
#The proportion of failures in the sample of 86 is 19:
[tex]\hat p=\frac{19}{86}\\\\=0.2209[/tex]
The z-value is calculated as:
[tex]z=\frac{\hat p-p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}[/tex]
[tex]=\frac{0.2209-0.45}{\sqrt{\frac{0.45(1-0.45)}{86}}}\\\\\\=-4.2706[/tex]
-4.2706 is less than the stated confidence level for the given 45% proportion and greatly differs from it.
- Reject the null hypothesis as there is enough evidence to reject the claim.
-Hence,Yes, Professor Brown can conclude that percentage of failures differs from 45%.
What do 2+e(6-7)? Everybody is saying it’s 2 but idk
Answer:
-0.71828
Step-by-step explanation:
2 + e(6-7)
2 + e(-1)
2 -e
e is approximately 2.718281828459045235360287471352662497757247093699959574966
2 - 2.71828.....
-0.71828
Answer:
2.37 (3 sf)
Step-by-step explanation:
2 + e^(6-7)
2 + e^(-1)
2 + 1/e (exact)
Roughly, 2.367879441
The angle measures in a triangle are 25°, 135°, and 20°. What type of triangle is it?
acute triangle
right triangle
obtuse triangle
isosceles triangle this is very confusing to me lol
The type of triangle is,
⇒ A scalene triangle
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The angle measures in a triangle are 25°, 135°, and 20°.
Now, We have alL angles are different to each other.
Hence, By definition of a scalene triangle,
The type of triangle is,
⇒ A scalene triangle
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A builder makes all of their ramps with a base to height ratio of 12:112:112, colon, 1 to be wheelchair-accessible. See the diagram below, which is not drawn to scale:
A certain ramp needs to cover a height of 0.80.80, point, 8 meters.
What is the length \ellℓell of this ramp?
Round your answer to the nearest hundredth of a meter.
The length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.
Pythagoras theorem states that, right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
A builder makes all the ramps with a base to height ratio of 12 to 1 to be wheelchair accessible.
Let p is the factor of ratio. Thus, the height and base is,
h = p
b = 12p
According to Pythagoras theorem,
unknown side (say l) is hypotenuse
l² = (12p)² + p²
[tex]l^2=144p+p^2[/tex]
[tex]l = \sqrt{144p+p^2}[/tex]
[tex]l = \sqrt{145} p[/tex]
A ramp needs to cover a height of 0.8 m. Height is equal to the factor p.
Thus, the value of p is,
p = h
p = 0.80
Thus, the length of the l is,
[tex]l = \sqrt{145} p[/tex]
[tex]l = \sqrt{145} {(0.8)}[/tex]
[tex]l=(12.041)(0.8)[/tex]
[tex]l=9.63m[/tex]
Hence, the length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.
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The correct question has in the image below
The two graphs below compare the gallons of gasoline used and the total distance traveled for two different cars.
Car 1
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 50) and (4, 100).
Car 2
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 40) and (4, 80).
Which comparison of the slopes of the two lines is accurate?
The comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.
Step 1:
The comparison of the slopes of the two lines can be made by calculating the slope of each line. Let's calculate the slopes:
For Car 1:
The coordinates are (2, 50) and (4, 100).
Using the slope formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex]:
[tex]\[ m = \frac{100 - 50}{4 - 2} = \frac{50}{2} = 25 \][/tex]
For Car 2:
The coordinates are (2, 40) and (4, 80).
Using the slope formula:
[tex]\[ m = \frac{80 - 40}{4 - 2} = \frac{40}{2} = 20 \][/tex]
Step 2:
Comparing the slopes:
- The slope of the line for Car 1 is 25.
- The slope of the line for Car 2 is 20.
Therefore, the comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.
Determine the simple interest earned on $21,500 after 16 years if the APR is 9 %.
The student asked about the simple interest earned on an investment. The simple interest can be calculated using the formula I = PRT. For a principal of $21,500 at a 9% APR for 16 years, the interest earned is $30,960.
Explanation:To calculate simple interest, you can use the formula I = PRT, where I is the interest, P is the principal amount (the initial amount of money), R is the rate of interest per period, and T is the time the money is invested for.
In this case, we have:
P (Principal) = $21,500R (Rate) = 9% or 0.09T (Time) = 16 yearsPlugging these values into the formula, we get:
I = PRT
I = $21,500 × 0.09 × 16
I = $30,960
The simple interest earned after 16 years is $30,960.
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Final answer:
The simple interest on $21,500 at 9% APR over 16 years is calculated using the formula I = PRT, which gives us a total interest of $30,960.
Explanation:
To calculate the simple interest earned on a sum of money, we can use the formula I = PRT, where I stands for interest, P for principal amount, R for the annual interest rate (in decimal form), and T for the time in years. In this case, the student wants to determine the interest earned on $21,500 at 9% APR for 16 years.
First, convert the interest rate from a percentage to a decimal by dividing by 100:
R = 9% / 100 = 0.09
Next, apply the values to the simple interest formula:
I = PRT
I = $21,500 × 0.09 × 16
I = $30,960
Therefore, the total simple interest earned after 16 years is $30,960.
The correlation analysis assumes that the measurements have a bivariate normal distribution in the population. Select all of the features that define a bivariate normal distribution.
A) A cloud of points that is funnel shaped (wider at one end than the other)
B) A relationship between X and Y that is not linear
C) The frequency distributions of X and Y separately are normal
D) Either X or Y has a decidedly skewed distribution
E) The presence of outliers Bell-shaped probability distribution in two dimensions rather than one
D) A relationship between X and Y that is linear
Answer:
Bruh i got correlation hw that i posted on here too and nobody helped lol.
Step-by-step explanation:
Select three ratios that are equivalent to 8:20
A: 1:4
B: 4:10
C: 24:60
D: 2:5
E: 10:24
Answer:
8 to 20 1 to 4 4 to 10
Step-by-step explanation:
it was easy
The sum of 5 fifteens and 3 fifteens
Answer:
(5 x 15) + (3 x 15) = 120
Step-by-step explanation:
5 x 15 = 75
3 x 15 = 45
75 + 45 = 120
Hope this helps :)
Answer:
5 * 15 = 75
3 * 15 = 45
45 + 75 = 120
Step-by-step explanation:
When you have a equation like that, you need to multiply. It is a faster way to solve the problem.
You had 15 five times.
15+15+15+15+15= 75 It equals the same thing because it is the same as 5 * 15
Same for the three fifteens.
15+15+15= 45.
The sum of the whole equation is 120 because you add 75 and 45.
Hope this helps, have a good day/night. Stay safe and healthy!
XYZ has been rotated 90°, as shown in the diagram. What is the length of
Y'Z?
Help Idk the answer
Answer:
7
Step-by-step explanation:
3. Danielle wants to know if she is over paying her auto insurance compared to her colleagues. She sent out a survey to a randomly selected 50 colleagues through email, and 30 of them responded. Here is the summary of the responded data. Danielle is paying $476, please help Danielle to find out if she is over paying for her auto insurance. (No points will be given without necessary steps). Sample STD 75 Minimum 397 Maximum 447 663 (1) What are the sample and population of the study? (2) Conduct appropriate statistical inference to help Danielle to address her concerns. (3) Based on your inference, what type of error could occur? Explain the error using the context words.
Answer:
a) - The population consists of all of Danielle's colleagues that could have been one of the randomly surveyed 50.
- The sample is Danielle's 50 colleagues that she ramdomly sampled.
b) From the statistical test performed, there is significant evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.
c) Check Explanation
Step-by-step explanation:
The full complete, correct question is attached to the solution of this question.
a) The population is normally the extended distribution where every selected random sample is extracted from. So, for this question, the population will be all of Danielle's colleagues.
The sample is the subset distribution obtained from the population. In the question, it is stated explicitly that Danielle randomly picked 50 of her colleagues to participate in the survey. Hence, the sample is Danielle's 50 colleagues that she ramdomly sampled.
b) The appropriate statistical inference for this question is to carry out the t-test hypothesis test.
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, Danielle wants to prove that she is overpaying for her auto insurance compared to her colleagues.
So, the null hypothesis is that there is no significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.
That is, Danielle isn't overpaying for her auto insurance compared to her colleagues or better stated that her colleagues are paying more than or just about the same for auto insurance compared to her.
While, the alternative hypothesis is that there is significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.
Let μ be the mean Danielle's colleagues' auto insurance fees.
Mathematically,
The null hypothesis is represented as
H₀: μ ≥ 476
The alternative hypothesis is given as
Hₐ: μ < 476
To do this test, we will use the t-distribution because no information on the population standard deviation is known
So, we compute the t-test statistic
t = (x - μ₀)/σₓ
x = sample mean = $447
μ₀ = Danielle's auto insurance bill that we're comparing the sample against = $476
σₓ = standard error = [σ/√n]
σ = Sample standard deviation = $75
n = Sample size = 30 (30 colleagues got back to Danielle)
σₓ = [75/√30] = $13.693
t = (447 - 476) ÷ 13.693
t = -2.117 = -2.12
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 30 - 1 = 29
Significance level = 0.05 (Most hypothesis tests are carried out at this level of significance)
The hypothesis test uses a one-tailed condition because we're testing only in one direction. (Checking whether Danielle is overpaying or that the mean is of her colleagues' auto insurance fees is less than Danielle's)
p-value (for t = -2.12, at 0.05 significance level, df = 29, with a one tailed condition) = 0.021342
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.021342
0.021342 < 0.10
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.
c) The two type of errors associated with this test include the Type I and Type II errors.
In Hypothesis testing, A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.
A type II error involves failing to reject the null hypothesis when in reality it should have been rejected. It entails not rejecting the null hypothesis and making conclusions based on the null hypothesis, when in reality, the alternative hypothesis should have been accepted together with its conclusion.
For this question, a type I error entails obtaining from the statistical test that Danielle is overpaying when she isn't overpaying for her auto insurance compared to her colleagues in reality.
A type II error would be obtaining from the statistical test that Danielle isn't overpaying when she is truly overpaying for her auto insurance compared to her colleagues, in reality.
Hope this Helps!!!
A wheel, which is part of a game at a shopping center is arranged to give 2 tickets 50% of the time, 5 tickets 25% of the time, 10 tickets 23% of the time, and 10 tickets 2% of the time. A player enters the shopping center and spins the wheel. Calculate the expected number of tickets he will get.
Answer:
The expected number of tickets a customer will get is 4.75.
Step-by-step explanation:
The probability distribution of the number of ticket a wheel at a shopping center is arranged to give is as follows:
X Probability (p)
2 0.50
5 0.25
10 0.23
10 0.02
The formula to compute the expected value of a random variable is:
[tex]E(X)=\sum x\cdot P (X=x)[/tex]
Compute the expected number of tickets a customer will get as follows:
[tex]E(X)=\sum x\cdot P (X=x)[/tex]
[tex]=(2\times 0.50)+(5\times 0.25)+(10\times 0.23)+(10\times 0.02)\\=1+1.25+2.3+0.2\\=4.75[/tex]
Thus, the expected number of tickets a customer will get is 4.75.
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
A. 168 degrees
B. 175 degrees
C. 150 degrees
D. 180 degrees
Answer:
(D) 180 degrees
Step-by-step explanation:
There are 12 hours on the clock.
For each 1 hour, the hour hand rotates = [tex]360^0 \div 12=30^0[/tex]
From 8 o'clock in the morning to 2 o'clock in the afternoon= 6 Hours
Therefore:
Number of degrees rotated by the hour hand = [tex]6 X 30^0 =180^0[/tex]
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.7 inches, and standard deviation of 5.2 inches. What is the probability that the height of a randomly chosen child is between 49.5 and 67.2 inches? Do not round until you get your your final answer, and then round to 3 decimal places.
Answer:
[tex]P(49.5<X<67.2)=P(\frac{49.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{67.2-\mu}{\sigma})=P(\frac{49.5-55.7}{5.2}<Z<\frac{67.2-55.7}{5.2})=P(-1.192<z<2.212)[/tex]
[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)[/tex]
[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)=0.987-0.117=0.870[/tex]
Step-by-step explanation:
We define X the random variable that represent the heights of a population for ten year old children, and for this case we know the distribution for X is given by:
[tex]X \sim N(55.7,5.2)[/tex]
Where [tex]\mu=55.7[/tex] and [tex]\sigma=5.2[/tex]
We want to find this probability:
[tex]P(49.5<X<67.2)[/tex]
We can use the z score formula to solve this problem given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we have:
[tex]P(49.5<X<67.2)=P(\frac{49.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{67.2-\mu}{\sigma})=P(\frac{49.5-55.7}{5.2}<Z<\frac{67.2-55.7}{5.2})=P(-1.192<z<2.212)[/tex]
And we can find this probability with this difference
[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)[/tex]
We can use tables for the normal standard distribution, excel or a calculator and we got this
[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)=0.987-0.117=0.870[/tex]
Find the point estimate for the true difference between the given population means. Round your answer to three decimal places.
(HINT: The point estimate for the difference between the population means is found by simply subtracting one sample mean from the other.)
Sample 1: Weights (in Grams) of Soap Bar A:
129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127
_____________________________________________________________
Sample 2: Weights (in Grams) of Soap Bar B:
131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131
Answer:
Point Estimate for different between population means = - 0.99
Step-by-step explanation:
We are given data of two samples and we have to find the best point estimate of the true difference between two population means. Remember that in absence of data about population the best estimator is the sample data. So, we will find the means of both sample data and find the difference of that means. This difference between the means of sample data will be the best point estimate for the true difference between the population means.
Formula to calculate the mean is:
[tex]Mean=\frac{\text{Sum of Values}}{\text{Number of Values}}[/tex]
Mean of Sample 1:
[tex]Mean=\frac{1414}{11}=128.55[/tex]
Mean of Sample 2:
[tex]Mean=\frac{1684}{13}=129.54[/tex]
Therefore the best point estimate for difference between two population means would be = Mean of Sample 1 - Mean of Sample 2
= 128.55 - 129.54
= - 0.99
Final answer:
The point estimate for the true difference between the given population means is -1.028.
Explanation:
The point estimate for the true difference between the given population means can be found by subtracting one sample mean from the other. Let's calculate it:
Sample 1: 129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127
Sample 2: 131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131
Sample mean of Sample 1 = (129+127+129+129+128+130+127+129+128+131+127)/11 = 128.818
Sample mean of Sample 2 = (131+126+132+129+128+131+131+130+128+129+126+132+131)/13 = 129.846
Point estimate for the difference = Sample mean of Sample 1 - Sample mean of Sample 2 = 128.818 - 129.846 = -1.028
This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane. -28 -54 -21 -40 -14 -26 What is the y-intercept of the line?
Answer:
The y-intercept is y = 2
Step-by-step explanation:
A linear function has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept, which is the value of y when x = 0.
We are given these three points:
(-28, -54)
(-21, -40)
(-14, -26)
We use two of them to build a system, to find values for m and b.
(-28, -54)
This means that when [tex]x = -28, y = -54[/tex]
So
[tex]y = mx + b[/tex]
[tex]-54 = -28m + b[/tex]
[tex]28m = b + 54[/tex]
[tex]m = \frac{b + 54}{28}[/tex]
(-21, -40)
This means that when [tex]x = -21, y = -40[/tex]
So
[tex]y = mx + b[/tex]
[tex]-40 = -21m + b[/tex]
[tex]-40 = -21\frac{b + 54}{28} + b[/tex]
[tex]-40 = \frac{-21b - 1134 + 28b}{28}[/tex]
[tex]7b - 1134 = -40*28[/tex]
[tex]7b = 14[/tex]
[tex]b = \frac{14}{7}[/tex]
[tex]b = 2[/tex]
The y-intercept is y = 2
Answer:
y = (0,2)
Step-by-step explanation:
Need help with this
What is the area of the following shape?
Answer:
114 square meters
Step-by-step explanation:
formula:1/2×h(a+b)
1/2×12{(12+5)+12}
1/2×12(17+12)
=6×19
=114m^2