AQR Stats - 5.4 - Central Limit Theorem-Apr 13

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

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

• The Population
• The Sample
• The Sampling Distribution

The weights of unicorns are given by N(1000, 25). What is the probability that a unicorn weighs less than 975 pounds?

• 15.87%
• 84.13%
• 46.02%
• 12.05%

Tags

CCSS.HSS.ID.A.4

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

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

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

What is the standard deviation of the distribution?

• 1010
• 20
• 60
• √20

A soft drink bottler claims that, on average, cans contain 12 oz. of soda. Suppose the true distribution of soda volumes is normally distributed with a mean of 12 oz. and a standard deviation of .16 oz. Sixteen cans are randomly selected and their volumes are measured. What is the probability the average volume will be between 11.96 and 12.08 oz.?

• .2902
• .8186
• .7424
• .3194

Tags

CCSS.HSS.ID.A.4

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?

• Approximately 0.15

• Approximately 0.43

• Approximately 0.57

• Approximately 0.85

REVIEW!

Find the area of the shaded region if the z-score is -0.3

• 0.6179

• 0.488

• 0.3783

• 0.3821