Sampling Distributions and the Central Limit Theorem

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?

• 400

• 40

• 25

• 8

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?

• 400

• 40

• 25

• 8

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?

• .0057

• .025

• .345

• .781

True or False:

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

• True

• False

The Central Limit Theorem states that if a population is (approximately) normal OR the sample size is greater than or equal to ____, then the associated sampling distribution is approximately normal.

• 30

• 20

• 500

• 80

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?

• .236

• .429

• .571

• .614

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.

• Central Limit Theorem

• Normal Distribution

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

• It becomes narrower and bimodal.

• It becomes narrower and more normal.

• It becomes wider and skewed right. 

• It becomes wider and more normal. 

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

• The Population

• The Sample

• The Sampling Distribution

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?

• .430

• .148

• .281

• .087