Normal Distributions 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

According to the Central Limit Theorem, For a sample to be large enough, the sample size should be ______.

• half of the population

• 75% of the population size

• at least 30

• at most 100

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

• 0.1151

• 0.2743

• 0.7257

• 0.8849

• Based on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated.

What is the standard deviation of the distribution?

• 1010

• 20

• 60

• √20

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

• 0.6915

• 0.3085

• 0.0228

• 0.2858

Find the area of the shaded region if the z-score is 0.75

• 0.2266

• 0.7734

• 0.758

• 0.242

A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test?

• 82

• 88

• 100

• 118

Yearling Angus steers had a mean weight of 1152 pounds with a standard deviation of 84 pounds. What's the actual weight of an animal whose z-score is - 1.5?

• 1026 pounds

• 1278 pounds

• 1020 pounds

• 1050 pou

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

• 68%

• 34%

• 16%

• 2.5%