Question 1

Egg weights The weights of hens' eggs are normally distributed with a mean of 56 grams
and a standard deviation of 4.8 grams. What is the probability that a dozen randomly
selected eggs weighs over 690 grams?

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Question 2

What is the probability that there is at least one customer to win a 50% discount among the
first five customers that enter the store?

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Question 3

What is the probability that the first customer to win a 30% discount is the sixth customer
that enters the store?

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Question 4

As you enter the store you watch the four people in front of you all win 50% discounts. The
store manager tells you how lucky you are to be throwing the cube while it is on a hot
streak, but the friend with you says you're unlucky because the streak can't continue.
Comment on their statements.

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Question 5

What is the probability that none of the first three customers gets more than a 30%
discount?

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Question 6

We will test the hypothesis that $p = 60 \%$ versus $p > 60 \%$. We don't know it, but actually $p$ is $70 \%$. With which sample size and significance level will our test have the greatest power?
A) $\alpha = 0.05 , n = 500$
B) $\alpha = 0.01 , n = 200$
C) $\alpha = 0.01 , n = 500$
D) The power will be the same so long as the true proportion $p$ remains $70 \%$.
E) $\alpha = 0.05 , n = 200$

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Question 7

Five

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Question 8

What is the probability that two customers in a row get only 10% discounts?

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Question 9

Approval rating A newspaper article reported that a poll based on a sample of 800 voters
showed the President's job approval rating stood at 62%. They claimed a margin of error of $$\pm 3 \%$$ 
%. What level of confidence were the pollsters using?

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Question 10

Roadblocks From time to time police set up roadblocks to check cars to see if the safety
inspection is up to date. At one such roadblock they issued tickets for expired inspection
stickers to 22 of 628 cars they stopped.
a. Based on the results at this roadblock, construct and interpret a 95% confidence interval
for the proportion of autos in that region whose safety inspections have expired.
b. Explain the meaning of "95% confidence" in part a).

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Question 11

Births A city has two hospitals, with many more births recorded at the larger hospital than
at the smaller one. Records indicate that in general babies are about equally likely to be
boys or girls, but the actual gender ratio varies from week to week. Which hospital is more
likely to report a week when over two-thirds of the babies born were girls? Explain.

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Question 12

15. Baldness and heart attacks A recent medical study observed a higher frequency of
heart attacks among a group of bald men than among another group of men who were not
bald. Based on a P-value of 0.062 the researchers concluded there was some evidence that
male baldness may be a risk factor for predicting heart attacks. Explain in this context what
their P-value means.

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Question 13

What is the probability that a customer gets more than a 20% discount?

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Question 14

Housing costs A government report on housing costs says that single-family home prices
nationwide are skewed to the right, with a mean of $235,700. We want to see how home
prices in Orange County, California compare with those nationwide.
a. We collect price data from a random sample of 50 homes in Orange County, California.
Why is it okay to use these data for inference even though the population is skewed?
b. The standard deviation of the 50 homes in our sample was $25,500. Specify the sampling
model for the mean price of such samples.
c. This sample of randomly chosen homes produced a 90% confidence interval for the
mean price in Orange County of ($233954, $246046). Does this interval provide evidence
that single-family home prices are unusually high in this county? Explain briefly.
d. Suppose we want to collect a new sample. How many homes must we survey to have
90% confidence of estimating the mean local price to within $2000?

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Question 15

The Masterfoods company manufactures bags of Peanut Butter M&M's. They report that
they make 10% each brown and red candies, and 20% each yellow, blue, and orange
candies. The rest of the candies are green.
a. If you pick a Peanut Butter M&M at random, what is the probability that
i. it is green?
ii. it is a primary color (red, yellow, or blue)?
iii. it is not orange?
b. If you pick four M&M's in a row, what is the probability that
i. they are all blue?
ii. none are green?
iii. at least one is red?
iv. the fourth one is the first one that is brown?
c. After picking 10 M&M's in a row, you still have not picked a red one. A friend says that
you should have a better chance of getting a red candy on your next pick since you have
yet to see one. Comment on your friend's statement.

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Question 16

What is the probability that a customer gets less than a 20% discount?

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Question 17

What is the probability that a customer gets at least a 40% discount?

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Question 18

A wildlife biologist wants to determine the mean weight of adult red squirrels. She captures 10 Squirrels she believes to be representative of the species and weighs them, finding a mean of 12.32 Grams and standard deviation of 1.88gm. Assuming these squirrels can be considered a random Sample of all red squirrels which of the following formulas gives a 95% confidence interval for the Mean weight of all squirrels? 
A) $12.32 \pm 2.262 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$
B) $12.32 \pm 2.228 \left( \frac { 1.88 } { \sqrt { 9 } } \right)$
C) $12.32 \pm 2.262 \left( \frac { 1.88 } { \sqrt { 9 } } \right)$
D) $12.32 \pm 2.228 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$
E) $12.32 \pm 1.96 \left( \frac { 1.88 } { \sqrt { 10 } } \right)$

Accepted Answer

The formula for a 95% confidence interval for the mean is:mean +/- z-score * (standard deviation / square root of sample size)where the z-score for a 95% confidence interval is 1.96.Plugging in the given values, we get:12.32 +/- 1.96 * (1.88 / square root of 10)which simplifies to:12.32 +/- 2.262 * (1.88 / 3.162)which further simplifies to:12.32 +/- 2.262 * 0.594which gives us a confidence interval of:12.32 +/- 1.34Therefore, the correct answer is A.

Question 19

What is the probability that the first two customers both get a 50% discount?

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Question 20

What is the probability that three consecutive customers all get 20% discounts?

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Quiz 8: Regression, Associations, and Predictive Modeling

Egg weights The weights of hens' eggs are normally distributed with a mean of 56 grams and a standard deviation of 4.8 grams. What is the probability that a dozen randomly selected eggs weighs over 690 grams?

What is the probability that there is at least one customer to win a 50% discount among the first five customers that enter the store?

What is the probability that the first customer to win a 30% discount is the sixth customer that enters the store?

As you enter the store you watch the four people in front of you all win 50% discounts. The store manager tells you how lucky you are to be throwing the cube while it is on a hot streak, but the friend with you says you're unlucky because the streak can't continue. Comment on their statements.

What is the probability that none of the first three customers gets more than a 30% discount?

We will test the hypothesis that $p = 60 \%$ versus $p > 60 \%$ . We don't know it, but actually $p$ is $70 \%$ . With which sample size and significance level will our test have the greatest power?

Five

What is the probability that two customers in a row get only 10% discounts?

Approval rating A newspaper article reported that a poll based on a sample of 800 voters showed the President's job approval rating stood at 62%. They claimed a margin of error of $\pm 3 \%$ %. What level of confidence were the pollsters using?

What is the probability that a customer gets more than a 20% discount?

What is the probability that a customer gets less than a 20% discount?

What is the probability that a customer gets at least a 40% discount?

What is the probability that the first two customers both get a 50% discount?

What is the probability that three consecutive customers all get 20% discounts?

Quiz 8: Regression, Associations, and Predictive Modeling

Egg weights The weights of hens' eggs are normally distributed with a mean of 56 grams and a standard deviation of 4.8 grams. What is the probability that a dozen randomly selected eggs weighs over 690 grams?

What is the probability that there is at least one customer to win a 50% discount among the first five customers that enter the store?

What is the probability that the first customer to win a 30% discount is the sixth customer that enters the store?

As you enter the store you watch the four people in front of you all win 50% discounts. The store manager tells you how lucky you are to be throwing the cube while it is on a hot streak, but the friend with you says you're unlucky because the streak can't continue. Comment on their statements.

What is the probability that none of the first three customers gets more than a 30% discount?

We will test the hypothesis that p=60%p = 60 \%p=60% versus p>60%p > 60 \%p>60% . We don't know it, but actually ppp is 70%70 \%70% . With which sample size and significance level will our test have the greatest power?

Five

What is the probability that two customers in a row get only 10% discounts?

Approval rating A newspaper article reported that a poll based on a sample of 800 voters showed the President's job approval rating stood at 62%. They claimed a margin of error of ±3%\pm 3 \%±3% %. What level of confidence were the pollsters using?

What is the probability that a customer gets more than a 20% discount?

What is the probability that a customer gets less than a 20% discount?

What is the probability that a customer gets at least a 40% discount?

What is the probability that the first two customers both get a 50% discount?

What is the probability that three consecutive customers all get 20% discounts?

We will test the hypothesis that $p = 60 \%$ versus $p > 60 \%$ . We don't know it, but actually $p$ is $70 \%$ . With which sample size and significance level will our test have the greatest power?

Approval rating A newspaper article reported that a poll based on a sample of 800 voters showed the President's job approval rating stood at 62%. They claimed a margin of error of $\pm 3 \%$ %. What level of confidence were the pollsters using?