Answer to Question #232446 in Management for nat

Question

3.2 Norman is a student at a college in Durban. The amount of time, in minutes, that Norman

walks to the college for his final examinations is constantly distributed between 15 to 40

minutes, inclusive. Use this information to answer the following questions.

3.2.1 Name the continuous probability distribution described above. Explain in detail why it

is called the distribution of little information. (3)

3.2.2 Calculate the probability that the student will take between 28 and 38 minutes. Provide

interpretation for your answer. (2)

3.2.3 Find the probability that the student will take no more than 30 minutes to arrive at the

college. Provide interpretation for your answer. (2)

3.2.4 Compute the probability that Norman will take least 35 minutes to get to the college.

Provide interpretation for your answer. (2)

3.2.5 Calculate the mean, variance and the standard deviation of the distribution described

in 3.2.

Answer 1

3.2.1

This is the uniform distribution since the probability is constant between 15 and 40 minutes.

3.2.2

= P(20<x<38)

probability = (38-28)/(40-15)

= 10/25

= 0.4

The probability to the student taking between 28 and 38 minutes to arrive is 0.4

3.2.3

= P(x≤30)

probability = (30-15)/(40-15)

= 15/25

= 0.4

The probability to the student will take less than 30 minutes to arrive is 0.6

3.2.4

= P(x≥30)

probability = (40-35)/(40-15)

= 0.2

The probability that Norman will take at least 35 minutes to arrive is 0.2