Normal Distributions and Central Limit Theorem

A population of students have a mean age of 15.8 years with a standard deviation of 0.6 years. The ages are normally distributed. What age represents the 90th percentile?

• 17.196

• 15.0311

• 16.569

• None of these

Samples of size 25 are drawn from a population where the mean and standard deviation of a population are 400 and 40, respectively.

What is the standard error, $\sigma_{\overline{x}}$ , of this sampling distribution?

• 400

• 40

• 25

• 8

Samples of size 25 are drawn from a population where the mean and standard deviation of a population are 400 and 40, respectively.

What is the mean,  $\mu_{\overline{x}}$ ,  of this sampling distribution?

• 400

• 40

• 25

• 8

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

• The Population Distribution

• The Sample Distribution

• The Sampling Distribution

• The Binomial Distribution

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?

• .00571

• .655

• .345

• .994

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

State whether you would use the central limit theorem or the normal distribution:
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that one egg selected at random from a hen house will weigh more than 68 grams?

• Central Limit Theorem
• Normal Distribution

Tags

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.4

State whether you would use the central limit theorem or the normal distribution:
The weights of the eggs produced by a certain breed of hen are normally distributed with mean 65 grams and standard deviation of 5 grams.
What is the probability that the average weight of a dozen eggs selected at random will be more than 68 grams? 

• Central Limit Theorem
• Normal Distribution

Tags

CCSS.HSS.ID.A.4

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. Find the probability that the SUM of the ages is between 9,800 and 9,900 years.

• 0.864

• 0.879

• 0.952

• None of these

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

• The Population Distribution

• The Sample Distribution

• The Sampling Distribution

• The Binomial Distribution