Exam 5: Continuous Random Variables

The weight of a product is normally distributed with a mean of four grams and a variance of .25 "squared grams." What is the probability that a randomly selected unit from a recently manufactured batch weighs: -More than 3.75 grams?

A probability distribution that is useful in describing the time or space between successive occurrences of an event is the _______ probability distribution.

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

Suppose the distribution of personality test scores is normally distributed with a mean of 15 and a variance of 25. -If X is an exponential random variable,then the probability X falls below its mean value is _____.

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?

At a Great Lakes nuclear power plant, lake water is used as part of the cooling system. This raises the temperature of the water that is discharged back into the lake. The amount that the water temperature is raised has a uniform distribution over the interval from 10 to 25º C. -What is the standard deviation of the temperature increase?

In a statistical study,the random variable X = 1,if the house is colonial,and X = 0 if the house is not colonial,then it is appropriate to model this variable with a continuous probability distribution.

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

The price of an energy sports drink is normally distributed with an average of $2.25 and a standard deviation of $0.15 across store outlets. -What is the probability that a randomly selected drink will cost between $2.00 and $3.00?

If the random variable of x is normally distributed,____ % of all possible observed values of x will be within two standard deviations of the mean.

At a Great Lakes nuclear power plant, lake water is used as part of the cooling system. This raises the temperature of the water that is discharged back into the lake. The amount that the water temperature is raised has a uniform distribution over the interval from 10 to 25º C. -Suppose that a temperature increase of more than 18 º C is considered to be potentially dangerous to the environment.What is the probability that at any point of time,the temperature increase is potentially dangerous?

The weight of a product is normally distributed with a mean of four grams and a variance of .25 "squared grams." What is the probability that a randomly selected unit from a recently manufactured batch weighs: -The weight of a product is normally distributed with a standard deviation of .5 grams.What should the average weight be if the production manager wants no more than 10% of the products to weigh more than 4.8 grams?

Is no more than 3 minutes?

What is the probability that the temperature increase will be less than 20º C?

Suppose that in an effort to provide better service to the public,the manager of the pizza delivery service is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time.The director decides that 15% of the customers should receive this discount.What are the number of minutes they need to wait to receive the discount?

The time of travel from a person's apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes.If they leave home at 9:05 AM,what is the probability that they will get to the station between 9:25 and 9:30 AM?

Suppose that the waiting time for a pizza to be delivered to an individual's residence 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

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

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 mean and median are the same for an exponential distribution.