Question

Suppose your friend is always between 11 and 16 minutes late. Within this range, it's equally likely that they will appear at any time. Use this information to answer the following.

A)What type of distribution best fits your friend's arrival pattern?

B)What is the probability that your friend will be between 13 and 15 minutes late? Express your answer as a simplified fraction.

C)What is the probability that your friend will be between 12 and 15 minutes late? Express your answer as a simplified fraction.

D) What is the probability that your friend will be more than 15 minutes late? Express your answer as a simplified fraction.

E)What is the probability your friend is exactly 11 minutes late?

Answer 1

(A) It is a uniform distibution case because the probability is equally likely that they will appear at any time

(B) probability that your friend will be between 13 and 15 minutes late

using

here we have y = 15, x = 13 and a = 11, b =16

we get

=(15-13)/(16-11)

= 2/5

(C) probability that your friend will be between 12 and 15 minutes late

using

here we have y = 15, x = 12 and a = 11, b =16

we get

=(15-12)/(16-11)

= 3/5

(D) probability that your friend will be more than 15 minutes late

using

here we have y = 15 and a = 11, b =16

we get

=(16-15)/(16-11)

= 1/5

(E) probability your friend is exactly 11 minutes late

using

here we have x = 11, a = 11 and b = 16

probability for any x value between 11 and 16 is exactly same because it is uniform distribution which has equal probability.

= 1/(16-11)

= 1/5