1)A recent report in BusinessWeek indicated that 32 percent of all employees steal from their company each year.

If a company employs 50 people, what is the probability that:

(a)

fewer than 11 employees steal?

(b)

more than 11 employees steal?

(c)

exactly 11 employees steal?

(d)

more than 11 but fewer than 21 employees steal?

2. The mean of a normal probability distribution is 380; the standard deviation is 8.

(a)

About 68 percent of the observations lie between what two values?

(b)

About 95 percent of the observations lie between what two values?

(c)

Practically all of the observations lie between what two values?

Best Electronics, Inc. offers a "no hassle" returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.0 per day and the standard deviation is 2.5 per day.

(a)

In what percent of the days are there 7.5 or fewer customers returning items?

(b)

In what percent of the days are between 13 and 15 customers returning items?

(c)

Is there any chance of a day with no returns?

Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 37.9 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 6.9 minutes.

(a)

What percent of the New York City commutes are for less than 29 minutes?

(b)

What percent are between 29 and 35 minutes?

(c)

What percent are between 29 and 42 minutes?

A normal population has a mean of 21 and a standard deviation of 5.

(a)

Compute the z value associated with 25

(b)

What proportion of the population is between 21 and 25?

(c)

What proportion of the population is less than 17?

For the most recent year available the mean annual cost to attend a private university in the United States was $20,107. Assume the distribution of annual costs follows a normal probability distribution and the standard deviation is $4,475.

Ninety-nine percent of all students at private universities pay less than what amount?

Customers experiencing technical difficulty with their Internet cable hookup may call an 800 number for technical support. It takes the technician between 90 seconds to 12 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

(a)

What are the values for a and b in minutes?

(b-1)

What is the mean time to resolve the problem?

(b-2)

What is the standard deviation of the time?

(c)

What percent of the problems take more than 5 minutes to resolve?

(d)

Suppose we wish to find the middle 50 percent of the problem-solving times. What are the end points of these two times?

The number of viewers of American Idol has a mean of 23 million with a standard deviation of 6 million. Assume this distribution follows a normal distribution.

What is the probability that next week's show will:

(a)

Have between 27 and 35 million viewers?

(b)

Have at least 15 million viewers?

(c)

Exceed 40 million viewers?

The closing price of Schnur Sporting Goods, Inc., common stock is uniformly distributed between $19 and 35 per share.Exercises

What is the probability that the stock price will be:

(a)

More than $27?

(b)

Less than or equal to $23?

Assume a binomial probability distribution with and .

Compute the following:

(a)

The mean and standard deviation of the random variable.

(b)

The probability that X is 13 or more.

(c)

The probability that X is 7 or less.

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,325. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 695 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 95 percent of the time?

Dotties Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 12 percent of the returns she prepared last year. Assuming this rate continues into this year and she prepares 57 returns. What is the probability that she makes errors on:

(a)

More than 8 returns?

(b)

At least 8 returns?

(c)

Exactly 8 returns?