# Thread: Help Reviewing Central Limit Theorem Multiple Choice Questions

1. ## Help Reviewing Central Limit Theorem Multiple Choice Questions

Hi All, Can someone help me review my answers below? This is a practice quiz and I am unable to get a good score. I am not sure which question I am getting wrong. My answers are highlighted in bold.

Question 2

An insurance company has 150,000 automobile policyholders. The expected yearly claim per policyholder is \$540 with a standard deviation of \$300. The distribution is strongly skewed to the right. Assuming a sample size of 50, what is mean yearly claim of the sample distribution?

Question 2 options:

\$10.80

\$540

\$3000

Not enough information is given.

Question 3

What is the standard deviation of the sample distribution?

Question 3 options:

42

50

60

Not enough information is given.

Question 4

If you randomly select 50 policies, what is the probability that their mean yearly claims is greater than \$600.

Question 4 options:

Almost 0%

2.5%

7.9%

Not enough information is given

Question 5

What can you say about the distribution of the sample means?

Question 5 options:

It is skewed to the right, like the population distribution.

Because n is large, it approaches a normal curve.

Because n (50) is much less than the size of the population (150,000), the distribution is still skewed.

Not enough information is given.

Question 6

Sodas in a can are supposed to contain an average 12 oz. This particular brand demonstrates a normal distribution with a standard deviation of 0.1 oz and a mean of 12.1 oz. What is the sample mean when the size of the samples is 6?

Question 6 options:

12

12.1

3

Not enough information is given.

Question 7
What is the standard deviation of the sample distribution?

Question 7 options:

0.1

0.04

0.16

0.016

Question 8

What is the probability that the mean contents of a six-pack are less than 12 oz?

Question 8 options:

0.072%

2.65%

15.87%

Not enough information is given.

Question 9

What can you say about the distribution of the sample means?

Question 9 options:

Because n is large, it approaches a normal curve.

Because n is small, we cannot assume it is normal.

[B]Because the population distribution is normal, we can assume the distribution of the sample mean is normal.

Not enough information is given.

Question 10
A binomial setting arises when we perform several independent trials of the same chance process and record the number of times that a particular outcome occurs. The four conditions for a binomial setting are:
(mark all that apply)

Question 10 options:

Binary? The possible outcomes of each trial can be classified as “success” or “failure.”

Independent? Trials must be independent; that is, knowing the result of one trial must not have any effect on the result of any other trial.

Number? The number of trials n of the chance process must be fixed in advance.

Success? On each trial, the probability p of success must be the same.

Question 11

You decide to test a friend for ESP using a standard deck of 52 playing cards. Such a deck contains 13 spades, 13 hearts, 13 diamonds, and 13 clubs. You shuffle the deck, select a card at random, and ask your friend to tell you whether the card is a spade, heart, diamond, or club. After the guess, you return the card to the deck, shuffle the cards, and repeat the above. You do this 100 times. Let X be the number of correct guesses by your friend in the 100 trials. Assuming your friend does not have ESP, the standard deviation of X is:

Question 11 options:

4.33

18.75

5

Not enough information is given.

Question 12

There are 40 true/false questions on a quiz. Each question is worth 1 point. Suppose a student guesses the answer to each question. If the student needs to score 25 correctly to pass the quiz, what is the probability that she does so?

Question 12 options:

37.5%

5.7%

18.3%

Not enough information is given.

2. ## Re: Help Reviewing Central Limit Theorem Multiple Choice Questions

I only looked at Question 12 and it seems incorrect. Why did you think it was 37.5?

Hint, I believed you had the following probability based on randomly guessing to get it right:

dbinom(1,size=1,prob=0.25) = 0.25

3. ## Re: Help Reviewing Central Limit Theorem Multiple Choice Questions

Originally Posted by hlsmith
I only looked at Question 12 and it seems incorrect. Why did you think it was 37.5?

Hint, I believed you had the following probability based on randomly guessing to get it right:

dbinom(1,size=1,prob=0.25) = 0.25
Using the binomial distribution would make the most sense. Unfortunately that most correct answer isn't an option here. They are being asked to use the normal approximation to the binomial distribution (justified by the CLT) to get the answer here.

Apparently the logic behind 37.5% is "There are 15 point values that give a passing grade and 40 points total so the probability must be 15/40". That is wrong because each of those isn't equally likely. If somebody was guessing it's obviously less likely for them to get all 40 correct than for them to only get 20 of them correct.

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