5.2 The Uniform Distribution

The data that follow are the number of passengers on 35 different charter fishing boats. The sample mean = 7.9 and the sample standard deviation = 4.33. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. State the values of a and b. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation.

A distribution is given as X ~ U(0, 20). What is P(2 < x < 18)? Find the 90^th percentile.

The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between zero and 15 minutes, inclusive.

b. On the average, how long must a person wait? Find the mean, μ, and the standard deviation, σ.

Suppose the time it takes a nine-year old to eat a donut is between 0.5 and 4 minutes, inclusive. Let X = the time, in minutes, it takes a nine-year-old child to eat a doughnut. Then X ~ U(0.5, 4).

a. The probability that a randomly selected nine-year-old child eats a doughnut in at least two minutes is _______.

Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. Let X = the time, in minutes, it takes a student to finish a quiz. Then X ~ U(6, 15).

Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. Then find the probability that a different student needs at least eight minutes to finish the…

The distribution can be written as X ~ U(1.5, 4.5).

In this distribution, outcomes are equally likely. What does this mean?

The distribution can be written as X ~ U(1.5, 4.5).

What are the constraints for the values of x?

The distribution can be written as X ~ U(1.5, 4.5).

What is P(2 < x < 3)?

The distribution can be written as X ~ U(1.5, 4.5).

What is P(x = 1.5)?

The distribution can be written as X ~ U(1.5, 4.5).

Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet.

Use the following information to answer the next eight exercises. A distribution is given as X ~ U(0, 12).

What is b? What does it represent?

Use the following information to answer the next eight exercises. A distribution is given as X ~ U(0, 12).

What is the theoretical mean?

Use the following information to answer the next eight exercises. A distribution is given as X ~ U(0, 12).

Find the 40^th percentile.

Use the following information to answer the next 12 exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

In words, define the random variable X.

Use the following information to answer the next 12 exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

The interval of values for x is ______.

Use the following information to answer the next 12 exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

Write the probability density function.

Use the following information to answer the next 12 exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

Find the average age of the cars in the lot.

For each probability and percentile problem, draw the picture.

A random number generator picks a number from one to nine in a uniform manner.

1. X ~ _________
2. Graph the probability distribution.
3. f(x) = _________
4. μ = _________
5. σ = _________
6. P(3.5 < x < 7.25) = _________
7. P(x > 5.67)
8. P(x > 5|x > 3) = _________
9. Find the 90^th percentile.

For each probability and percentile problem, draw the picture.

A subway train arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.

1. Define the random variable. X = _______
2. X ~ _______
3. Graph the probability distribution.
4. f(x) = _______
5. μ = _______
6. σ = _______
7. Find the probability tha…

Use the following information to answer the next three exercises. The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

What is the average waiting time (in minutes)?

1. zero
2. two
3. three
4. four

Use the following information to answer the next three exercises. The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

The probability of waiting more than seven minutes given a person has waited more than four minutes is?

1. 0.125
2. 0.25
3. 0.5
4. 0.75

Use the following information to answer the next three exercises. The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

The number of miles driven by a truck driver falls between 300 and 700, and follows a uniform distribution.

1. Find the probability that th…