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A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. a. Compute the probability that 2 or fewer will withdraw. b. Compute the probability that exactly 4 will withdraw. c. Compute the probability that more than 3 will withdraw. d. Compute the expected number of withdrawals.

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 5.5, Problem 41E
Textbook Problem
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A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.

  1. a. Compute the probability that 2 or fewer will withdraw.
  2. b. Compute the probability that exactly 4 will withdraw.
  3. c. Compute the probability that more than 3 will withdraw.
  4. d. Compute the expected number of withdrawals.

a.

To determine

Find the probability that 2 or fewer will withdraw.

Explanation of Solution

Calculation:

It was found that 20% of the students withdraw without completing the introductory statistics course and the assumption is that 20 students registered for the course.

Define the random variable x as the numbers of students withdraw without completing the introductory statistics course. Here, a random sample (n) of 20 students is taken. Each student is independent of the other. Also, there are two possible outcomes, the students withdraw without completing the introductory statistics course or not (success or failure). It was found that 20% of the students withdraw without completing the introductory statistics course. Thus, the probability of success (p) is 0.20. Thus, x follows binomial distribution.

The probability of obtaining x successes in n independent trails of a binomial experiment is,

f(x)=(nx)px(1p)nx,x=0,1,2,...,n

Where, p is the probability of success.

Substitute values n=20 and p=0.20 in the above equation. Then,

f(x)=(20x)(0.20)x(10.20)20x

The probability that 2 or fewer will withdraw is the sum of the probabilities at the points x=0,x=1 and x=2. That is,

P(x2)=f(0)+f(1)+f(2)=[(200)(0

b.

To determine

Find the probability that exactly 4 will withdraw.

c.

To determine

Find the probability that more than 3 will withdraw.

d.

To determine

Find the expected number of withdrawals.

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