Question

A study of the time spent shopping in a supermarket for 20 specific items showed an approximately uniform distribution between 25 minutes and 45 minutes. a. s the probability that the shopping time will be between 28 and 36 minutes? b. What is the probability that the shopping time will be less than 40 minutes? c. What are What the mean and standard deviation of the shopping time? a. The probability that the shopping time will be between 28 and 36 minutes is (Type an integer or a decimal) b. The probability that the shopping time will be less than 40 minutes is (Type an integer or a decimal) C. The mean of the given uniform distribution is p (Type an integer or a decimal) The standard deviation of the given uniform distribution is o (Round to four decimal places as needed )

Answer 1

A) P(28 < X < 36)

= (36 - 28)/(45 - 25)

= 8/20 = 0.4

B) P(X < 40)

= (40 - 25)/(45 - 25)

= 15/20 = 0.75

C)  $\mu$ = (a + b)/2

= (25 + 45)/2

= 70/2 = 35

$\sigma$ = (b - a)/$\sqrt 12$

= (45 - 25)/$\sqrt 12$

= 20/$\sqrt 12$

= 5.7735