6-1 to 6-3 Normal Curve and Central limit theorem

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

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

• The Population
• The Sample
• The Sampling Distribution

Tags

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

Researchers 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?

• .7632
• .4290
• .5696
• .6664

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

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
• .2991
• .9943
• .7810

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?

• .8508
• .1492
• .2815
• .0872

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.3

Find the area of the shaded region if the z-score is -0.30.

• 0.6179
• 0.4880
• 0.3783
• 0.3821

Find the area of the shaded region if the z-score is 1.25.

• 0.1056
• 0.8944
• 0.8849
• 0.1151

Find the area of the shaded region if the z-scores are -0.25 and 1.

• 0.4400
• 0.8413
• 0.4013
• 0.1587

Find the area of the shaded region if the z-scores are -2 and -0.5

• 0.3313
• 0.3085
• 0.0228
• 0.2857

According to the central limit theorem, what happens to the sampling distribution of a sample mean as n increases?

• It becomes narrower and more skewed.

• It becomes more normal.

• It becomes wider and more skewed.