1-Why do most of the sample means differ somewhat

from the population mean? What is this difference

called?

2-What is the standard deviation of the sample means

called? What is the formula for this standard deviation?

3-Teachers Salaries in Connecticut The average

teachers salary in Connecticut (ranked first among

states) is $57,337. Suppose that the distribution of

salaries is normal with a standard deviation of $7500.

a. What is the probability that a randomly selected

teacher makes less than $52,000 per year?

b. If we sample 100 teachers salaries, what is the

probability that the sample mean is less than

$56,000?

14. SAT Scores The national average SAT score (for

Verbal and Math) is 1028. Suppose that nothing is

known about the shape of the distribution and that the

standard deviation is 100. If a random sample of 200

scores were selected and the sample mean were

calculated to be 1050, would you be surprised? Explain

16. Worker Ages The average age of chemical engineers

is 37 years with a standard deviation of 4 years. If an

engineering firm employs 25 chemical engineers, find

the probability that the average age of the group is

greater than 38.2 years old. If this is the case, would it

be safe to assume that the engineers in this group are

generally much older than average?

18. Medicare Hospital Insurance The average yearly

Medicare Hospital Insurance benefit per person was

$4064 in a recent year. If the benefits are normally

distributed with a standard deviation of $460, find the

probability that the mean benefit for a random sample

of 20 patients is

a. Less than $3800

b. More than $4100

21. Time to Complete an Exam The average time it takes

a group of adults to complete a certain achievement test

is 46.2 minutes. The standard deviation is 8 minutes.

Assume the variable is normally distributed.

a. Find the probability that a randomly selected adult

will complete the test in less than 43 minutes.

b. Find the probability that if 50 randomly selected

adults take the test, the mean time it takes the

group to complete the test will be less than

43 minutes.

c. Does it seem reasonable that an adult would finish

the test in less than 43 minutes? Explain.

d. Does it seem reasonable that the mean of the 50

adults could be less than 43 minutes?

25. Weekly Income of Private Industry Information

Workers The average weekly income of information

workers in private industry is $777. If the standard

deviation is $77, what is the probability that a random

sample of 50 information workers will earn, on average,

more than $800 per week? Do we need to assume a

normal distribution? Explain.