The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.6 years. The standard deviation of the distribution is 2.6 years.

For a random sample of 57 men, what is the likelihood that the age at which they were married for the first time is less than 24.8 years?(Round z value to 2 decimal places. Round your answer to 4 decimal places.)

Probability

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,200. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 820 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.

How many pages should the manufacturer advertise for each cartridge if it wants to be correct99 percent of the time?(Round z value to 2 decimal places. Round your answer to the nearest whole number.)

Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $5,870 per hour and a standard deviation of $417.

What is the operating cost for the lowest 5% of the airplanes?(Roundzvalue to 2 decimal places and round final answer to nearest whole dollar.)

A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 5.10 minutes and the standard deviation was 0.40 minutes.

a.	What fraction of the calls last between 5.10 and 5.80 minutes?(Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Fraction of calls

b.	What fraction of the calls last more than 5.80 minutes?(Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Fraction of calls

c.	What fraction of the calls last between 5.80 and 6.50 minutes?(Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Fraction of calls

d.	What fraction of the calls last between 4.50 and 6.50 minutes?(Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Fraction of calls

e.	As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 3 percent of the calls. What is this time?(Round z-score computation to 2 decimal places and your final answer to 2 decimal places.)

Duration