Exam 6: Continuous Probability Distributions

Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours.What is the probability that the battery will last more than 9 hours before running out of power?

The average time between trades for a high-frequency trading investment firm is 40 seconds.Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is less than 20 seconds?

The z table provides _________ probabilities for positive and negative values of z.

The time for a professor to grade a homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes.What is the probability that randomly selected homework will require less than 16 minutes to grade?

The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one.

The Japan Sumo Association has begun to measure the body fat of wrestlers to try to combat the growing problem of excessive obesity within the sport.As of 2010,the average wrestler weighed 412 pounds.Suppose the weights of sumo wrestlers are normally distributed,with a standard deviation of 37 pounds.What is the probability that a randomly selected wrestler weighs between 350 and 450 pounds?

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds.Find the mean and standard deviation of the waiting time.

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

Alex is in a hurry to get to work and is rushing to catch the bus.She knows that the bus arrives every six minutes during rush hour,but does not know the exact times the bus is due.She realizes that from the time she arrives at the stop,the amount of time that she will have to wait follows a uniform distribution with a lower bound of 0 minutes and an upper bound of six minutes.What is the probability that she will have to wait more than two minutes?

The time for a professor to grade a homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes.What is the probability that randomly selected homework will require between 11 and 15 to grade?

Suppose the amount of time customers must wait to check bags at the ticketing counter in Boston Logan Airport is exponentially distributed with a mean of 14 minutes.What is the probability that a randomly selected customer will have to wait more than 20 minutes?

The continuous uniform distribution describes a random variable,defined on the interval [a,b],that has an equally likely chance of assuming values within a specified range.

The average wait time at a McDonald's drive-through window is about three minutes ("The Doctor Will See You Eventually," The Wall Street Journal,October 18,2010).Suppose the wait time is exponentially distributed.What is the probability that a randomly selected customer will have to wait no more than five minutes?

An Excel's function NORMAL.DIST can be used to Compute probabilities for the normal distribution.

The normal distribution is _________ in the sense that the tails get closer and closer to the horizontal axis but never touch it.

A superstar major league baseball player just signed a new deal that pays him a record amount of money.The star has driven in an average of 110 runs over the course of his career,with a standard deviation of 31 runs.An average player at his position drives in 80 runs.What is the probability the superstar bats in fewer runs than an average player next year? Assume the number of runs batted in is normally distributed.

The cumulative distribution function F(x)of a continuous random variable X with the probability density function f(x)is which of the following?

The time for a professor to grade a homework in statistics is normally distributed with a mean of 12.6 minutes and a standard deviation of 2.5 minutes.What is the probability that randomly selected homework will require more than 12 minutes to grade?

The probability P(Z > 1.28)is closest to ____.

Jennifer is waiting for a taxi cab.The average wait time for a taxi is six minutes.Suppose the wait time is exponentially distributed.What is the probability that a taxi arrives in three minutes or less?