Exam 7: Continuous Random Variables

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will fewer than 160 boxes of supplies arrive in a week?

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the standard deviation of the water depth?

Find z when the area to the left of z is .6700.

The number of standard deviations that a value, x, is from the mean is a(n) ________.

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What proportion of students scored between 81 and 89?

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of .15 ounce. What is the probability that a randomly selected apple will contain more than 2.50 ounces?

At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C. What is the expected value of the temperature increase?

________ values of the standard deviation result in a normal curve that is narrower and more peaked.

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. Complete the following statement: Only 20 percent of the individuals wait less than ________ minutes.

Consider a normal population with a mean of 10 and a variance of 4. Find P(X ≥ 10).

The z value tells us the number of ________ that a value of x is from the mean.

A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers is a(n) ________ distribution.

At an oceanside nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C. What is the probability that the temperature increase will be between 20° and 22° C?

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. What is the probability of getting a grade of 91 or less on this exam?

If x is a binomial random variable where n = 100 and p = .1, find the probability that x is less than or equal to 10, using the normal approximation to the binomial.

Consider a normal population with a mean of 10 and a variance of 4. Find P(X < 6).

For a binomial probability experiment, with n = 150 and p = .2, it is appropriate to use the normal approximation to the binomial distribution.

A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is

The average time an individual reads online national news reports is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed. What is the probability someone will spend at least one hour reading online national news reports?

During the past six months, 73.2 percent of U.S. households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. Eighty percent of the households spent more than what amount?