Question

1.

Assume a normal distribution and find the following probabilities.

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x < 24 | μ = 27 and σ = 4)
enter the probability of fewer than 24 outcomes if the mean is 27 and the standard deviation is 4

(b) P(x ≥ 63 | μ = 50 and σ = 7)
enter the probability of 63 or more outcomes if the mean is 50 and the standard deviation is 7

(c) P(x > 46 | μ = 50 and σ = 6)
enter the probability of more than 46 outcomes if the mean is 50 and the standard deviation is 6

(d) P(23 < x < 27 | μ = 25 and σ = 4)
enter the probability of more than 23 and fewer than 27 outcomes if the mean is 25 and the standard deviation is 4

(e) P(x ≥ 84 | μ = 70 and σ = 2.77)
enter the probability of 84 or more outcomes if the mean is 70 and the standard deviation is 2.77

2.

In a recent year, the average daily circulation of the Wall Street Journal was 2,276,207. Suppose the standard deviation is 70,940. Assume the paper’s daily circulation is normally distributed.

(a) On what percentage of days would circulation pass 1,817,000?
(b) Suppose the paper cannot support the fixed expenses of a full-production setup if the circulation drops below 1,602,000. If the probability of this even occurring is low, the production manager might try to keep the full crew in place and not disrupt operations. How often will this even happen, based on this historical information?

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x > 1,817,000) = enter the probability that the daily circulation would pass 1,817,000
(b) P(x < 1,602,000) = enter the probability that the daily circulation will drop below 1,602,000

3.

According to the Air Transport Association of America, the average operating cost of an MD-80 jet airliner is $2,087 per hour. Suppose the operating costs of an MD-80 jet airliner are normally distributed with a standard deviation of $163 per hour.

(Round the value of z to 2 decimal places. Round your answers to 2 decimal places.)

(a) At what operating cost would only 20% of the operating costs be less?

$enter the dollar amount at which only 20% of the operating costs would be less

(b) At what operating cost would 65% of the operating costs be more?

$enter the dollar amount at which 65% of the operating costs would be more

(c) What operating cost would be more than 85% of operating costs?

$enter the dollar amount that would be more than 85% of operating costs

4.

The U.S. Bureau of Labor Statistics released hourly wage figures for various countries for workers in the manufacturing sector. The hourly wage was $30.67 for Switzerland, $20.20 for Japan, and $23.82 for the U.S. Assume that in all three countries, the standard deviation of hourly labor rates is $4.00.

Appendix A Statistical Tables

a. Suppose 43 manufacturing workers are selected randomly from across Switzerland and asked what their hourly wage is. What is the probability that the sample average will be between $30.00 and $31.00?
b. Suppose 35 manufacturing workers are selected randomly from across Japan. What is the probability that the sample average will exceed $21.00?
c. Suppose 48 manufacturing workers are selected randomly from across the United States. What is the probability that the sample average will be less than $22.75?

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

a. enter the probability that the sample average will be between $30.00 and $31.00 supposing that 43 manufacturing workers are selected randomly from across Switzerland
b. enter the probability that the sample average will exceed $21.00 supposing that 35 manufacturing workers are selected randomly from across Japan
c. enter the probability that the sample average will be less than $22.75 supposing that 48 manufacturing workers are selected randomly from across the United States

Answer 1