Answer:
0.6848
Step-by-step explanation:
Mean of \hat{p} = 0.453
Answer = 0.453
Standard deviation of \hat{p} :
= \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} = \sqrt{\frac{0.453(1-0.453)}{100}} = 0.0498
Answer = 0.0498
P(0.0453 - 0.05 < p < 0.0453 + 0.05)
On standardising,
= P(\frac{0.0453-0.05-0.0453}{0.0498} <Z<\frac{0.0453+0.05-0.0453}{0.0498})
= P(-1.0044 < Z < 1.0044) = 0.6848
Answer = 0.6848
Using the Central Limit Theorem, it is found that the mean of the sampling distribution of the sample proportions is 0.453.
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 a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem:
Sample of 100, thus [tex]n = 100[/tex].Proportion of 45.3%, thus [tex]p = 0.453[/tex].By the Central Limit Theorem, the mean is [tex]\mu = p = 0.453[/tex].
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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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In order for a constitutional amendment to the Florida constitution to pass 60% of the popular vote must support the amendment. A researcher is interested in determining if the more than sixty percent of the voters would support a new amendment about higher education. The researcher asks 500 random selected potential voters if they would support the amendment. Define the parameter.
Answer:
p=population of Floridians that would support the amendment
Step-by-step explanation:
we are given parameters are,
n = Sample size = 500
and p = Population proportion = 60% = 0.6
p = the population proportion of Floridians that would the amendment.
Answer:
A
Step-by-step explanation:
The complete question is:
In order for a constitutional amendment to the Florida constitution to pass 60% of the popular vote must support the amendment. A researcher is interested in determining if the more than sixty percent of the voters would support a new amendment about higher education. The researcher asks 500 random selected potential voters if they would support the amendment. Define the parameter.
A) phat= sample proportion of 500 Floridans that would support the ammendment
B) p= population proportion of Floridans that would support the ammendment
C) phat= population proportion of Floridans that would support the ammendment
D) p= sample proportion of 500 Floridans that would support the ammendment
p is the actual probability of an event which is 0.6
phat is the value calculated from the sample observation
here a sample of 500 Floridans is taken and probability from sample is being observed. So phat is the parameter which is the population proportion of 500 Floridans that would support the ammendment
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]
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.
A package contains 4 red, 2 green, 8 purple, and 6 blue jelly beans. What is the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean?
The probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is 12/95.
The probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is the product of the probability of choosing a purple jelly bean and the probability of choosing a blue jelly bean given that a purple jelly bean was already chosen.
The probability of choosing a purple jelly bean is 8/20 = 2/5.
The probability of choosing a blue jelly bean given that a purple jelly bean was already chosen is 6/19. This is because there are only 6 blue jelly beans left after the purple jelly bean is eaten, and there are a total of 19 jelly beans left.
Therefore, the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is 2/5 * 6/19 = 12/95.
Another way to solve this problem is to use the following formula:
P(A and B) = P(A) * P(B | A)
Where:
P(A) is the probability of event A happening
P(B | A) is the probability of event B happening given that event A already happened
In this case, event A is choosing a purple jelly bean and event B is choosing a blue jelly bean.
Therefore, the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is:
P(purple jelly bean) * P(blue jelly bean | purple jelly bean) = 2/5 * 6/19
= 12/95.
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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]
A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches. a study participant is randomly sleected. what height cuts off the top 5%
Answer:
The height that cuts off the top 5% is 74.83 inches.
Step-by-step explanation:
We are given that in the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches.
Let X = heights of respondents
So, X ~ N([tex]\mu=69.9,\sigma^{2} =3^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean height = 69.9 inches
[tex]\sigma[/tex] = standard deviation = 3.0 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, we have to find the height that cuts off the top 5%, that means;
P(X > [tex]x[/tex]) = 0.05 {where [tex]x[/tex] is the height that cuts off top 5%}
P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{ x -69.9}{3}[/tex] ) = 0.05
P(Z > [tex]\frac{ x -69.9}{3}[/tex] ) = 0.05
Now, in the z table the critical value of X that gives the area of top 5% is given as 1.6449.
So, [tex]\frac{ x -69.9}{3} = 1.6449[/tex]
[tex]x -69.9= 1.6449 \times 3[/tex]
[tex]x[/tex] = 69.9 + 4.9347 = 74.83
Hence, the height that cuts off the top 5% is 74.83 inches.
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.
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.
How do i know if 4/6 < 3/10?
Answer:
4/6 > 3/10
Step-by-step explanation:
4/6 < 3/10
First get a common denominator of 30
4/6 *5/5 < 3/10 *3/3
20/30 < 9/30
This is false since 20 > 9
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
Solve: (1/8)^-3a=512
Answer:
a = 1
Step-by-step explanation:
The problem is written as a linear equation:
((1/8)^-3)a = 512
512a = 512 . . . . simplify
a = 1 . . . . . . . . . divide by the coefficient of a
___
We suspect you might intend the exponential equation:
(1/8)^(-3a) = 512
512^a = 512 . . . . . simplify
a = 1 . . . . . . . . . . . compare bases and exponents
equivalently, take the log to the base 512:
a·1 = 1
a = 1
Simplify.
(4x’y - 9xy + 4) + (-7r’y+ 4xy? + 8)
Answer:
4 y x ' − 9 x y − 7 y r ' + 4 x y? + 12
Step-by-step explanation:
Simplified the expression.
<3
Answer:
4 y x ' − 9 x y − 7 y r ' + 4 x y ? + 12
As Saturn revolves around the sun, it travels at a speed of approximately 6 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Saturn travel in 3 minutes?
Answer:360 miles per minute , and 1080 in 3 minutes
Step-by-step explanation:
Uta invests an amount into a compound interest investment account that pays 6% a year. After six years she withdraws her total balance of $500. Using the formula A=p(1+r)t how much money did Uta initially invest?
Uta initially invest $353, if she withdraws $500 after six years with compound interest of 6% a year.
Step-by-step explanation:
The given is,
After six years she withdraws her total balance of $500
Interest rate 6 % a year ( compounded )
Step:1
Formula to calculate the future amount with an compound interest rate,
[tex]F=P(1+r)^{t}[/tex].............................(1)
Where, F - Future worth amount
P - Initial investment
r - Rate of interest
t - No. of years
Step:2
From the given,
F = $500
r = 6%
t = 6 years
Equation (1) becomes,
[tex]500 = P(1+0.06)^{6}[/tex]
= [tex]P(1.06)^{6}[/tex]
= P (1.41852)
[tex]P= \frac{500}{1.41852}[/tex]
= 352.48
≅ 353
P = $353
Result:
Uta initially invest $353, if she withdraws $500 after six years with compound interest of 6% a year.
Answer:
C- $352.48
Step-by-step explanation:
Just took test :]
The quotient of a number increased by 13 and -7 is -4
The number in question is found by setting up the equation (x + 13) / -7 = -4, and solving for 'x'. Following order of operations and sign rules, we determine that the number is 15.
Explanation:The question asks us to find a number when given that the quotient of that number increased by 13 and -7 is -4. To solve this, we set up an equation and follow the multiplication and division rules for signs and the order of operations.
Let the unknown number be 'x'. According to the problem, (x + 13) / -7 = -4. Multiplying both sides by -7 to eliminate the denominator, we get x + 13 = (-7)(-4). Applying the rule that the product of two negative numbers is positive, we simplify the right side to get x + 13 = 28. Now, we subtract 13 from both sides to isolate 'x': x = 28 - 13, which gives us x = 15.
The number in question is therefore 15.
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)
8/12 - 2/12 =
THIS IS WORTH 100pts the only question pleaseeeeee
Answer:
1/2
Step-by-step explanation:
Since they have the same denominator, you can just subtract the numerators. So, 8-2=6.
6/12 can be simplified to 1/2.
Answer:
the answer is 1/2 or 0.5
Step-by-step explanation:
hope this helps!
A shop has the following offers. Fig rolls (125g packet) Normal price £1.08. Buy one, get 2nd half price.
The total cost of two packets of fig rolls, with the second one at half price, is £1.62. The calculation involves the normal price of one packet plus half of that price for the second one.
Explanation:The question involves calculating the total cost of fig rolls when a shop offers a deal where if you buy one packet, you get the second packet at half the price.
To find the total cost of two packets under this offer, we first take the normal price of one packet (£1.08) and add it to half of that price (which is £1.08 / 2 = £0.54). The total cost for two packets is therefore £1.08 (first packet) + £0.54 (second packet at half price), which equals £1.62.
For 3 packets of fig rolls and 6 packets of crisps, the total price is £8.42 considering the offers of buy one, get 2nd half price and three for the price of two, respectively.
For the fig rolls:
Normal price for 1 packet = £1.08
Buy one, get 2nd half price.
So, for 3 packets of fig rolls, we'd pay for 2 and get the third at half price.
Total cost for 3 packets of fig rolls = Cost of 2 packets + Half price of 1 packet
[tex]= 2 \times £1.08 + \frac{1}{2} \times £1.08[/tex]
= £2.16 + £0.54
= £2.70
For the crisps:
Normal price for 1 packet = £1.43
Three for the price of two.
So, for 6 packets of crisps, we'd pay for 4 and get 2 free.
Total cost for 6 packets of crisps = Cost of 4 packets
[tex]\(= 4 \times £ 1.43\)[/tex]
= £5.72
Therefore, the total price for 3 packets of fig rolls and 6 packets of crisps would be:
Total = Cost of 3 fig roll packets + Cost of 6 crisps packets
= £2.70 + £5.72
= £8.42
Complete Question:
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!
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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of the 85 points scored by the hpa thunderbirds , jayla scored 20%. how many points did jayla score?
Answer:
17 points
Step-by-step explanation:
20% × 85 = 0.20 × 85 = 17
Jayla scored 17 points.
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
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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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%.
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!!!
Select a composite number to break into factors. Continue
factoring until all factors are prime.
Final answer:
To factor a composite number into primes, divide it by its smallest divisor that is not 1, then continue dividing the quotient until all factors are prime. An example is the number 60, which factors into 2 x 2 x 3 x 5, or 2² x 3 x 5 when using exponents for the repeated factor of 2.
Explanation:
The subject of the question is to select a composite number and break down its factors until all the factors are prime. As an example, let's choose the composite number 60. Here's how you can factor it into primes:
First, note that 60 is an even number, so it is divisible by 2. Start by dividing 60 by 2 to get 30.
Now, 30 is still even, so we can divide by 2 again to get 15.
15 is divisible by 3, so when we divide it by 3, we get 5, which is a prime number.
So, the prime factorization of 60 is 2 x 2 x 3 x 5, often written using exponents for any repeated factors as 22 x 3 x 5.
Through factorization, we have converted the composite number into a product of prime factors. Each factor multiplication is a step that requires one to find two numbers that multiply to the number we are factoring and continuing this process until we reach numbers that are prime.
Solve the equation using the distributive property and properties of equality.
-5(a + 3) = -55
What is the value of a?
O a
Ob
-14
-8
d
14
Answer:
a =8
Step-by-step explanation:
-5(a + 3) = -55
Distribute
-5a -15 = -55
Add 15 to each side
-5a-15+15 = -55+15
-5a = -40
Divide each side by -5
-5a/-5 = -40/-5
a = 8
solve -6 4/9-3 2/9-82/9
Answer: The final answer in proper fraction is 169/9
Step-by-step explanation:
Given the expression
-6 4/9-3 2/9-82/9
Firstly let us convert all mixed fraction to proper fraction to further simplify the expression
-58/9 - 29/9 - 82/9
We now have all terms in proper fraction, we can continue by finding the LCM which is 9
= (- 58-29-82)/9
= 169/9
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: