Normal Distributions and Central Limit Theorem

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. 

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 deviation (also called the standard error) of the sampling distribution?

• 400

• 40

• 25

• 8

 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?

• 0.864
• 0.879
• 0.121
• None of these

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

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

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

True or False:

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

• True

• False

True or False:

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

• True

• False

True or False:

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

• True

• False