Quiz about Central Limit Theorem

Question 1

What happens to the shape of a sampling distribution of sample means as n increases?

Accepted Answer

It becomes narrower and more normal.

Answer

It becomes narrower and bimodal.

Answer

It becomes wider and skewed right.

Answer

It becomes wider and more normal.

Question 2

The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25.
What is the mean of the sampling distribution?

Accepted Answer

400

Answer

40

Answer

25

Answer

8

Question 3

The mean and standard deviation of a population are 400 and 40, respectively. Sample size is 25.
What is the standard error of the sampling distribution?

Accepted Answer

8

Answer

400

Answer

40

Answer

25

Question 4

A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years.  The ages are normally distributed. What is the probability that a randomly selected student is older than 16.5 years old?

Accepted Answer

0.121

Answer

0.864

Answer

0.879

Answer

None of these

Question 5

These symbols represent the mean and standard deviation for which of the following distributions?

Accepted Answer

The Population

Answer

The Sample

Answer

The Sampling Distribution

Question 6

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons.  What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?

Accepted Answer

.0057

Answer

.025

Answer

.345

Answer

.781

Question 7

Researches found that boys playing high school football absorb an average of 355 hits to the head with a standard deviation of 80 hits during a season.  What is the probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360?

Accepted Answer

.571

Answer

.236

Answer

.429

Answer

.614

Question 8

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours.  What is the probability that a randomly selected group of 35 high school students get more than 6 hours of sleep each night?

Accepted Answer

.148

Answer

.430

Answer

.281

Answer

.087

Question 9

True or False:

As the sample size n increases without limit, the shape of the distribution becomes less normal.

Accepted Answer

False

Answer

True

Question 10

True or False:

The number of samples for sampling with replacement may be computed by multiplying the sample size to the population size.

Accepted Answer

False

Answer

True

Question 11

True or False:

The mean of the sample means is equal to the mean of the population.

Accepted Answer

True

Answer

False

Question 12

True or False:

Whatever is the distribution of the population if sample size is increased, the distribution will become approximately normal.

Accepted Answer

True

Answer

False

Question 13

True or False:

The variance of the sampling distribution is equal to the population variance multiplied by the sample size.

Accepted Answer

False

Answer

True

Question 14

State whether you would use the central limit theorem or the normal distribution:
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that one egg selected at random from a hen house will weigh more than 68 grams?

Accepted Answer

Normal Distribution

Answer

Central Limit Theorem

Question 15

State whether you would use the central limit theorem or the normal distribution:
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that the average weight of a dozen eggs selected at random will be more than 68 grams?

Accepted Answer

Central Limit Theorem

Answer

Normal Distribution

Question 16

State whether you would use the central limit theorem or the normal distribution:
In a study done on the life expectancy of 500 people in a certain geographic region, the mean age at death was 72 years and the standard deviation was 5.3 years.
If a sample of 50 people from this region is selected, and the probability that the mean life expectancy will be less than 70 years.

Accepted Answer

Central Limit Theorem

Answer

Normal Distribution

Central Limit Theorem

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