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Homework 2

1.

The number of semester hours of college credit taken by CFA candidates has a distribution with

a mean of 141 hours and a standard deviation of 18 hours. Consider a random sample of 100

first-time candidates for the CFA exam and let represent the mean number of hours of college

credit taken for the sample.

a.

What if uz?

b. What is oz?

C.

Describe the shape of the sampling distribution of x.

d.

Find the z-score for the value i = 142 hours.

Find P(x > 142)

1

ECON 15B

2. The Food and Drug Administration is checking the amount of cereal that a breakfast food company

is putting in their boxes. The packaging process for the breakfast cereal has been adjusted so that

566 grams of cereal is supposed to be dispensed into each box. The standard deviation for the

population is unknown, but the standard deviation from a sample of 49 boxes is 56 grams. What

is the probability that anywhere from 550 and 574 grams on average is dispensed in each box?

Answer: Probability that anywhere from 550 and 574 grams on average is dispensed in each box

is

ECON 15B

2. The Food and Drug Administration is checking the amount of cereal that a breakfast food company

is putting in their boxes. The packaging process for the breakfast cereal has been adjusted so that

566 grams of cereal is supposed to be dispensed into each box. The standard deviation for the

population is unknown, but the standard deviation from a sample of 49 boxes is 56 grams. What

is the probability that anywhere from 550 and 574 grams on average is dispensed in each box?

Answer: Probability that anywhere from 550 and 574 grams on average is dispensed in each box

is

3. Assume that the amount of time an Internal Revenue Service examiner is supposed to spend

reviewing a randomly selected return is 55.1 minutes, with a standard deviation of about 17.6

minutes. If a sample of 35 such reviews is selected, what is the probability that the average review

time is more than an hour?

Answer: The probability that the average review time is more than an hour is

2

Answer: The probability that the average review time is more than an hour is

2

ECON 15B

4. In a study of factors that affect whether students return to college after the first semester, one of

the factors examined was the number of hours worked per week. The analysis revealed that

students typically work an average of 18.1 hours per week, with a standard deviation of 15.3

hours. If we consider a group of 700 freshmen at a community college, what is the probability that

the average number of hours worked per week is more than 20 hours?

Answer: The probability that the average number of hours worked per week is more than 20

hours is

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Tags:

standard deviation

probability

economics

Normal Distribution

Sampling distribution

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