Question

Suppose your friend is always between 7 and 12 minutes late. Within this range, it's equally likely that they will appear at any time. Use this information to answer the following.

Step 1 of 5: What type of distribution best fits your friend's arrival pattern?

Step 2 of 5:

What is the probability that your friend will be between 9 and 11 minutes late? Express your answer as a simplified fraction.

Step 3 of 5:

What is the probability that your friend will be between 8 and 11 minutes late? Express your answer as a simplified fraction.

Step 4 of 5:

What is the probability that your friend will be more than 11 minutes late? Express your answer as a simplified fraction.

Step 5 of 5:

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

Answer 1

(A) It is uniform disitribution because it is equally likely between 7 and 12 minutes

probability density = 1/(b-a)................where b = 12 and a = 7

= 1/(12-7)

= 1/5

(B) probability that your friend will be between 9 and 11 minutes late

Interval of probability distribution = difference between 9 and 11 = 2

So, probability = (Interval of probability distribution)*(probability density) = 2*(1/5) = 2/5

(C) probability that your friend will be between 8 and 11 minutes late

Interval of probability distribution = difference between 8 and 11 = 3

So, probability = (Interval of probability distribution)*(probability density) = 3*(1/5) = 3/5

(D) probability that your friend will be more than 11 minutes late

Interval of probability distribution = difference between 11 and 12(upper level) = 1

So, probability = (Interval of probability distribution)*(probability density) = 1*(1/5) = 1/5

(E) Probability of exactly 11 is equal to the probability density

So, P(x = 11) = probability density

= 1/(12-7)

= 1/5