Free Printable Normal Distributions and Central Limit Theorem

Worksheets

Normal Distributions and Central Limit Theorem

Total questions: 10

Worksheet time: 50mins

Name

Class

Date

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

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

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

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

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