Exam 6: Continuous Random Variables

Given the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet,what is the probability he throws it: No less than 55 feet?

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?

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. Only 5% of the students taking the test scored higher than what grade?

The probability that an appliance is in repair is .5.If an apartment complex has 100 such appliances,what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial.

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 he/she leaves home at 9:05 AM,what is the probability that he/she will get to the station between 9:25 and 9:30 AM?

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?

During the past six months,73.2% of US households purchased sugar.Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10.80% of the households spent more than what amount?

The exponential probability distribution is based on a continuous random variable.

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

Consider a normal population with a mean of 10 and a standard deviation 2. Find P(X > 13).

The specific shape of each normal distribution is determined by its _____ and _____.

At an ocean-side 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 25ºC. What is the probability that the temperature increase will be less than 20ºC?

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 within 1 standard deviation of the mean?

At an ocean-side 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 25ºC. What is the expected value of the temperature increase?

The weight of a product is normally distributed with a mean of four 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?

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 weekly be greater than 210 or Less than 180?

The number of defective pencils in a lot of 1000 is an example of a continuous random variable.

The mean and median are the same for a normal distribution.

Find z when the area between z and - z is .9030

The actual weight of hamburger patties is an example of a continuous random variable.