Question

The commute time to work for a particular employee follows a continuous uniform distribution with a minimum time of 15 minutes and a maximum time of 29 minutes. Complete parts a-f.

a) Calculate the value of f(x).
f(x) = 0.071
(Type a decimal rounded to three decimal places as needed.)

b) What are the mean and standard deviation for this distribution?
The mean of this distribution is 22 minutes.
(Type an integer or decimal rounded to two decimal places as needed.)
The standard deviation of this distribution is ? minutes.
(Type an integer or decimal rounded to two decimal places as needed.)
Find standard deviation

Answer 1

For a continuous uniform distribution, we calculate the value of f(x) by finding the length of the range and dividing it by the total range of the distribution. The mean of this distribution is 22 minutes and the standard deviation is 14 / sqrt(12).

Step-by-step explanation:

In a continuous uniform distribution, the probability density function f(x) is constant within the range of the distribution and zero outside of that range.

To calculate the value of f(x) for this particular distribution, we need to find the length of the range and divide it by the total range of the distribution.

In this case, the range is from 15 minutes to 29 minutes, so the length of the range is 29 - 15 = 14 minutes.

Dividing this length by the total range of the distribution (29 - 15 = 14 minutes), we get f(x) = 1/14 = 0.071.

The mean of a continuous uniform distribution is given by the formula mean = (minimum + maximum) / 2. So the mean for this distribution is (15 + 29) / 2 = 22 minutes.

The standard deviation of a continuous uniform distribution is given by the formula standard deviation = (maximum - minimum) / sqrt(12).

Substituting the given values, we get standard deviation = (29 - 15) / sqrt(12) = 14 / sqrt(12).