# Sampling distribution

1. On a national standardized test with a normal distribution of scores, a mean of 50, and a standard deviation of 3.2, a student's score is 1.2 standard deviations above the mean.

What is the students score?

2. A national achievement test has a normal distribution, a mean of 1000, and a standard deviation of 100. What percent, to the nearest whole percent, of the students taking the test scored above 800?

3. Which of the following statements summarizes the Law of Large Numbers?

A. The random sample mean will converge in probability to the distribution mean if the sample is sufficiently large.

B. The random sample mean will diverge in probability to the distribution mean if the sample is sufficiently large.

C. The random sample variance will converge in probability to the distribution mean if the sample is sufficient large.

D. The random sample variance will converge in probability to the distribution variance if the sample is sufficiently large.

E. The random sample variance will diverge in probability to the distribution mean if the sample is sufficiently large.

4. An educator is conducting a survey of students at the educator's university. The educator mails a survey to a random sample of the students, but only 20% of the surveys are returned.

What could the educator do to compensate for the poor return rate? (select 3)

a. offer some valuable reward for completing the survey

b. send reminders or make follow-up calls to non-respondents

c. adjust the findings to compensate for any sample imbalance.

d. use each survey response twice in the data analysis

e. find substitute subjects in classes taught by the educator

f. change sample size equal to the number of respondents

#### Solution Summary

The solution provides step by step method for the calculation of sampling distribution . Formula for the calculation and Interpretations of the results are also included.