Exam 7: Continuous Random Variables

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 less than 3.60 m?

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. Ninety-nine percent of the households spent less than what amount?

Which of the following is a continuous distribution?

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. For the 10 percent who spend the most time reading national news online, how much time do they spend?

For a continuous distribution, the exact probability of a particular value is zero.

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 more than 5 ounces?

The grade a student received on an examination was transformed to a z value, which was negative. Therefore, we know that the student scored

What is the probability that a standard normal random variable will be between .3 and 3.2?

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 received in a week exceed 200?

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 $16.00 on sugar.

Find z when the area to the right of z is .1314.

The thickness of a randomly selected metal piece is a ________ random variable.

An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed. What proportion of tests has scores over 90?

A probability distribution that describes the time or space between successive occurrences of an event is a(n) ________ probability distribution.

The weight of a product is normally distributed with a mean of 4 ounces and a variance of .25 squared ounces. The company wants to classify the unit as a scrap in a maximum of 1 percent of the units if the weight is below a desired value. Determine the desired weight such that no more than 1 percent of the units are below it.

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 no more than 30 minutes reading online national news reports?

Find z when the area between 0 and z is .4750.

The time between breakdowns of an alarm system is exponentially distributed with mean 10 days. What is the probability that there is less than 1 breakdown on a given day?

The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time is between 2 and 4 minutes?

For a continuous distribution, P(X ≤ 100) = P(X < 100).