Exam 7: Continuous Random Variables

A continuous probability distribution that has a rectangular shape, where the probability is evenly distributed over an interval of numbers, is called a uniform probability distribution.

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. In an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15 percent of the customers should receive this discount. What number of minutes do they need to wait to receive the discount?

A standard normal distribution has a mean of ________ and standard deviation of ________.

Consider a normal population with a mean of 10 and a variance of 4. Find P(X > 7).

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. Find the probability that a household spent more than $10.00 on sugar.

The weight of a product is normally distributed with a mean of 5 ounces. A randomly selected unit of this product weighs 7.1 ounces. The probability of a unit weighing more than 7.1 ounces is .0014. The production supervisor has lost files containing various pieces of information regarding this process, including the standard deviation. Determine the value of the standard deviation for this process.

The mean of a standard normal distribution is always equal to ________.

The ________ is a graphic that is used to visually check whether data come from a normal population.

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 less than 800 hours?

The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. We calculated the value of z for a specific box of this brand of cereal, and the z value was negative. This negative z value indicates that

The area under the curve of a valid continuous probability distribution must ________.

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 less than 4.66 hours?

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 from the population is between 30.25 and 30.65 inches long?

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 percentage of students scored between 65 and 89?

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. Find the probability that a household spent less than $5.00 on sugar.

The weight of a product is normally distributed with a mean of 4 ounces and a variance of .25 squared ounces. What is the probability that a randomly selected unit from a recently manufactured batch weighs no more than 3.5 ounces?

When a ________ probability distribution is used to approximate a ________ probability distribution, we must make a ________ correction.

The weight of a product is normally distributed with a standard deviation of .5 ounces. What should the average weight be if the production manager wants no more than 5 percent of the products to weigh more than 5.1 ounces?

The local airport in a Midwestern state keeps track of the percentage of flights arriving within 15 minutes of their scheduled arrivals. The stem-and-leaf plot of the data for one year is below. Construct a normal probability plot and interpret the plot.

The mean of a standard normal distribution is always equal to 1.