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Statistics Multiple Choice Questions with Answers

## Central Limit Theorem

1. Multiple Choice

1.The Central Limit Theorem is important in statistics because _____.
(A)for a large n, it says the sampling distribution of the sample mean is approximately normal,
regardless of the distribution of the population
(B)for any population, it says the sampling distribution of the sample mean is approximately
normal, regardless of the sample size
(C)for a large n, it says the population is approximately normal
(D)for any size sample, it says the sampling distribution of the sample mean is approximately
normal

2.In point estimation

(A)data from the sample is used to estimate the population parameter
(B)data from the sample is used to estimate the sample statistic
(C)the mean of the population equals the mean of the sample
(D)data from the population is used to estimate the population parameter

3.A recent study suggested that 70% of all eligible voters will vote in the next presidential election.
Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Which of the following represent part of what is necessary for this problem to be analyzed using the binomial probability distribution?

I.   There are two outcomes possible for each of the 20 voters sampled.
II.  The outcomes of the 20 voters must be considered independent of one another.
III. The variable is continuous.

(A) I only
(B)  II only
(C) III only
(D) I and II only
(E)  I and III only
(F) I, II, and III

4.Which of the following is not a characteristic of the normal probability distribution?
(A)The standard deviation is always equal to 0.
(B)The mean is equal to the median, which is also equal to the mode.
(C)Symmetry
(D)The total area under the curve is always equal to 1.

5.As the sample size increases, the
(A) standard error of the mean goes away
(B) standard error of the mean decreases
(C) standard error of the mean increases
(D) standard error of the mean does not change
6.Classify the following random variable according to whether it is discrete or continuous. (4 pts)
a)The blood pressures of a group of students the day before the final exam________________
b)The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska___________________
c)The number of cups of coffee sold in a cafeteria during lunch_________________________
d)The speed of a car on a Los Angeles freeway during rush hour traffic___________________

7.An automobile manufacturer has determined that 40% of all gas tanks that were installed on its 2002 compact model are defective. If 11 of these cars are independently sampled

a)What is the probability that exactly 5 of the gas tanks will be defective?

b)What is the expected number of gas tanks that are NOT defective?

8."DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed.

a)What percentage of all bottles produced contains more than 6.37 ounces of vitamins?

b)If you have 40 bottles of vitamins, how many would you expect to contain more than 6.37 ounces of vitamins?

c)The top ninety percent of the bottles will contain how many ounces?