Exam 6: Continuous Random Variables

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 a.m. ,what is the probability that he/she will get to the station between 9:25 and 9:30 a.m.?

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 no more than 3 minutes?

Find z when the area to the left of z is .6700.

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

A continuous probability distribution that is useful in describing the time or space between successive occurrences of an event is a(n):

An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state.The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.Between what two values (in ounces)symmetrically distributed around the population mean will 80 percent of the apples fall?

In a statistical study,the random variable X = 1 if the house is colonial,and X = 0 if the house is not colonial.The random variable X is continuous.

The US local airport 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. 76 9 77 114 78 79 07 80 88 81 2 82 1 83 88 Compute the standardized quartile value O_i for i = 4.

A normal distribution with mean equal to zero and a standard deviation equal to one is called the ____________ normal distribution.

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

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?

At an oceanside 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 25° C.What is the probability that the temperature increase will be less than 20° C?

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

The _____________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

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 3.75 ounces?

For a continuous random variable x,the height of the probability curve f(x)at a particular point indicates the value of the probability for that value.

At an oceanside 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 25°C.Suppose that a temperature increase of more than 18° C is considered to be potentially dangerous to the environment.What is the probability that at any point in time,the temperature increase is potentially dangerous?

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?

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.

For a binomial probability experiment,with n = 150 and p = .2,it is appropriate to use the normal approximation to the binomial distribution.