Question

Assume that the download times for a two-hour movie are uniformly distributed between 15 and 24 minutes. Find the following probabilities. a. What is the probability that the download time will be less than 16 minutes? b. What is the probability that the download time will be more than 23 minutes? c. What is the probability that the download time will be between 17 and 22 minutes? d. What are the mean and standard deviation of the download times? a. The probability that the download time will be less than 16 minutes is (Round to four decimal places as needed.) l. b. The probability that the download time will be more than 23 minutes is (Round to four decimal places as needed.) c. The probability that the download time will be between 17 and 22 minutes is (Round to four decimal places as needed.) d. The mean of the given uniform distribution is u = (Type an integer or a decimal.) The standard deviation of the given uniform distribution is a = 11 (Round to four decimal places as needed.)

Answer 1

Uniform distribution between a = 15 minutes and b = 24 minutes

a. P(less than 16 minutes) = P(X < 16)

= (16 - 15)/(24 - 15)

= 0.1111

b. P(more than 23 minutes) = P(X > 23)

= (24 - 23)/(24 - 15)

= 0.1111

c. P(between 17 and 22 minutes) = P(17 < X < 22)

= (22 - 17)/(24 - 15)

= 0.5556

d. Mean, $\small \mu$ = (15+24)/2

= 19.5 minutes

e. Standard deviation, $\small \sigma$ = $\small (b-a)/\sqrt{12}$

= $\small (24-15)/\sqrt{12}$

= 2.5981 minutes