Exam 7: Continuous Random Variables

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly more than 4.80 hours?

Given that X is a normal random variable, the probability that a given value of X is below its mean is ________.

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 between 2.00 and 3.00 ounces?

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. What is the probability that a sheet selected at random will be less than 29.75 inches long?

The price-to-earnings ratio for firms in a given industry is distributed according to the normal distribution. In this industry, a firm with a standard normal variable value of z = 1

Consider a normal population with a mean of 10 and a variance of 4. Find P(X > 18).

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last more than 1,200 hours?

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.

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 probability that a randomly selected depth is between 2.25 m and 5.00 m?

________ values of the standard deviation result in a normal curve that is wider and flatter.

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. What is the probability that a randomly selected individual will have a waiting time between 15 and 45 minutes?

A continuous random variable may assume only integer values in a given interval.

Suppose that the times required for a cable company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit will take at least 50 minutes?

The mean and the median are the same for an exponential distribution.

Which of the following statements is not a property of the normal probability distribution?

Suppose the daily change in price of a stock is normally distributed with mean = .20 and standard deviation = .30. What price change is associated with the 25th percentile?

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 the number of boxes of supplies that arrive be greater than 210 or less than 180?

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of .2 inches. What is the probability that a sheet selected at random will be less than 31 inches long?

Find z when the area to the left of z is .05.

What is the probability that a standard normal random variable will be between −2 and 2?