The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.7 years. The standard deviation of the distribution is 2.8 years.
For a random sample of 60 men, what is the likelihood that the age at which they were married for the first time is less than 25.2 years?
Probability
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 5.00 minutes and the standard deviation was 0.40 minutes.
a. What fraction of the calls last between 5.00 and 5.80 minutes?
b. What fraction of the calls last more than 5.80 minutes?
c. What fraction of the calls last between 5.80 and 6.50 minutes?
d. What fraction of the calls last between 4.50 and 6.50 minutes?
e. As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 6 percent of the calls. What is this time?
The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,300. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 720 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 correct 90 percent of the time?
Assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $5,957 per hour and a standard deviation of $492.
What is the operating cost for the lowest 5% of the airplanes?
A normal population has a mean of 20 and a standard deviation of 4.
a. Compute the z value associated with 24.
b. What proportion of the population is between 20 and 24?
c. What proportion of the population is less than 15?
According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 24 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.5.
What is the probability this could occur by chance?
The Internal Revenue Service is studying the category of charitable contributions. A sample of 34 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 34 returns, 8 had charitable contributions of more than $1,000. Suppose 7 of these returns are selected for a comprehensive audit.
a. You should use the hypergeometric distribution is appropriate. Because
(Click to select)you are sampling a small population without replacement.you are sampling a large population without replacement.you are sampling a small population with replacement.
b. What is the probability exactly one of the seven audited had a charitable deduction of more than $1,000?
c. What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?
The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience.
Admissions Probability
1,070 0.2
1,460 0.1
1,560 0.7
1. What is the expected number of admissions for the fall semester? Expected number of admissions
2. Compute the variance and the standard deviation of the number of admissions.