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 normal curve is symmetrical about the mean.

• True
• False

Suppose a student takes a standardized test measuring college level skills. Scores on the test are normally distributed with a mean of 500 and a standard deviation of 100. If the student scores 575,what is the corresponding z-score?

• 0.75
• -0.75
• 0.2
• 1.15

 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

What is the standard deviation of the distribution?

• 1010
• 20
• 60
• √20

The mean and standard deviation of a population are 200 and 20, respectively. 
What is the probability of selecting 25 data values with a mean less than 190?

• 69%
• 0.6%
• 31%
• 99%

Which sample size for a sampling distribution will have the SMALLEST standard deviation?

• n = 10
• n = 200
• n = 400
• n = 1000

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

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

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