QMB3200 Ch. 6 HW

Assume that the amount of time that it takes an employee to service a car at an oil change facility follows the uniform probability distribution between 21 and 38 minutes. What is the probability that a randomly selected car will require exactly 30 minutes to service?

0.0

John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes. What is the probability that the commute time for a randomly selected day will be less than 18 minutes?

0.044

During the 3 pm to 5 pm time period, cars arrive at a bank's drive-through window at an average rate of 15 customers per hour. Assume that the time between arrivals follows the exponential distribution. What is the probability that a randomly selected customer will arrive more than 10 minutes after the previous customer?

0.0821

Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between these two cities will be less than $300?

0.1015

Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between these two cities will be more than $450?

0.1796

Suppose the average tread-life of a certain brand of tire is 42,000 miles and that this mileage follows the exponential probability distribution. What is the probability that a randomly selected tire will have a tread-life between 30,000 and 50,000 miles?

0.1855

Assume that the amount of time that it takes an employee to service a car at an oil change facility follows the uniform probability distribution between 21 and 38 minutes. What is the probability that a randomly selected car will require less than 25 minutes to service?

0.2353

The time that customers wait to be served at the delicatessen for a grocery store follows the uniform distribution between 0 and 7 minutes. What is the probability that a randomly selected customer will wait less than 2 minutes at the deli?

0.2857

John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes. What is the probability that the commute time for a randomly selected day will be between 28 and 34 minutes?

0.3232

Assume that the flight time for U.S. Airways flight 1267 from Philadelphia to Dallas follows the uniform probability distribution between 210 and 250 minutes. What is the probability that a randomly selected flight will take less than 224 minutes?

0.35

Assume that the flight time for U.S. Airways flight 1267 from Philadelphia to Dallas follows the uniform probability distribution between 210 and 250 minutes. What is the probability that a randomly selected flight will take between 220 and 235 minutes?

0.375

Assume that the average talk time on an Apple iPhone is 20 hours and that this time follows the exponential probability distribution. What is the probability that a randomly selected iPhone will experience between 10 and 30 hours of talk time?

0.3834

During the 3 pm to 5 pm time period, cars arrive at a bank's drive-through window at an average rate of 15 customers per hour. Assume that the time between arrivals follows the exponential distribution. What is the probability that a randomly selected customer will arrive between 2 and 6 minutes after the previous customer?

0.3834

Suppose the average tread-life of a certain brand of tire is 42,000 miles and that this mileage follows the exponential probability distribution. What is the probability that a randomly selected tire will have a tread-life of more than 40,000 miles?

0.3858

The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes. What is the probability that a randomly selected exam will require between 14 and 19 minutes to grade?

0.4479

Assume that the amount of time that it takes an employee to service a car at an oil change facility follows the uniform probability distribution between 21 and 38 minutes. What is the probability that a randomly selected car will require more than 30 minutes to service?

0.4706

Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between these two cities will be between $325 and $425?

0.5275

Assume that the amount of time that it takes an employee to service a car at an oil change facility follows the uniform probability distribution between 21 and 38 minutes. What is the probability that a randomly selected car will require between 25 and 35 minutes to service?

0.5882

The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes. What is the probability that a randomly selected exam will require more than 15 minutes to grade?

0.6215

During the 3 pm to 5 pm time period, cars arrive at a bank's drive-through window at an average rate of 15 customers per hour. Assume that the time between arrivals follows the exponential distribution. What is the probability that a randomly selected customer will arrive less than 5 minutes after the previous customer?

0.7135

Suppose the average tread-life of a certain brand of tire is 42,000 miles and that this mileage follows the exponential probability distribution. What is the probability that a randomly selected tire will have a tread-life of less than 65,000 miles?

0.7872

The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes. What is the probability that a randomly selected exam will require less than 20 minutes to grade?

0.8108

Bob's golf score at his local course follows the normal distribution with a mean of 92.1 and a standard deviation of 3.8. What is the probability that the score on his next round of golf will be less than 100?

0.9812

John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes. The interval around the mean that contains 99.7% of the commute times is ________.

11.4, 42.0

Assume that the flight time for U.S. Airways flight 1267 from Philadelphia to Dallas follows the uniform probability distribution between 210 and 250 minutes. What is the standard deviation of this distribution?

11.55

The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes. The interval around the mean that contains 68% of the times needed to grade exams is ________.

12.1, 20.5

The time that customers wait to be served at the delicatessen for a grocery store follows the uniform distribution between 0 and 7 minutes. What is the mean of this distribution?

3.5

During the 3 pm to 5 pm time period, cars arrive at a bank's drive-through window at an average rate of 15 customers per hour. Assume that the time between arrivals follows the exponential distribution. What is the average time between customer arrivals?

4 minutes

During the 3 pm to 5 pm time period, cars arrive at a bank's drive-through window at an average rate of 15 customers per hour. Assume that the time between arrivals follows the exponential distribution. What is the standard deviation for this probability distribution?

4 minutes

Assume that the amount of time that it takes an employee to service a car at an oil change facility follows the uniform probability distribution between 21 and 38 minutes. What is the standard deviation of this distribution?

4.91

Bob's golf score at his local course follows the normal distribution with a mean of 92.1 and a standard deviation of 3.8. The interval around the mean that contains 68% of Bob's golf scores is ________.

88.3, 95.9

The exponential probability distribution is a discrete distribution that is often used to describe time between customer arrivals.

False

The z-score follows a normal distribution with μ = 1 and σ = 0, which is known as the standard normal distribution.

False

The time that customers wait to be served at the delicatessen for a grocery store follows the uniform distribution between 0 and 7 minutes. What is the probability that a randomly selected customer will wait more than 4 minutes at the deli?

NOT 0.5714

The area under the curve of the normal probability distribution is always equal to 1.0.

True

The left and right ends of the normal probability distribution extend indefinitely, never quite touching the horizontal axis.

True

The mathematical expression that describes the shape of the curve for the exponential distribution is known as the exponential probability density function.

True

The z-score in a normal probability distribution determines the number of standard deviations that a particular value, x, is from the mean.

True

With the continuous uniform probability distribution, the probability of any interval in the distribution is equal to any other interval with the same width.

True

A discrete random variable that follows the Poisson distribution with a mean equal to λ has a counterpart continuous random variable that follows the ________ distribution with a mean equal to μ = 1/λ.

exponential

The ________ probability distribution is used to describe data where lower values tend to dominate and higher values don't occur very often.

exponential

The shape of the uniform probability distribution is ________.

flat

The ________ probability distribution is bell-shaped and symmetrical.

normal

The shape of the exponential distribution is ________.

right-skewed

The ________ probability distribution describes data where all the values have the same chance of occurring.

uniform

Which of the following statements is true regarding z-scores for the normal probability distribution?

z-scores are negative for values of x that are less than the distribution mean.