Several million lottery tickets are sold, and 60% of the

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

ISBN: 9780073401331 38

Solution for problem 9E Chapter 4.2

Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

Several million lottery tickets are sold, and 60% of the Tickets are held by women. Five winning tickets will be drawn at random.

a. What is the probability that three or fewer of the winners will be women?

b. What is the probability that three of the winners will be of one gender and two of the winners will be of the other gender?

Step-by-Step Solution:

Answer :

Step 1 of 3:

Given, 60% of the tickets are held by women in several million lottery tickets and 5 winning tickets are drawn at random.

Let X follows binomial distribution with probability mass function is

P(x: n,p) = ${(}_{x}^{n})$ ${p}^{x}$ (1 - p ${)}^{(n-x)}$ , x = 0, 1, 2, ….., n.

Where,

n = sample size

= 5

x = random variable

p = probability of success

= 60%

= 0.60

q = 1 - p (probability of failure)

Mean of the binomial distribution is

${\mu{}}_{x}$ = np

Variance of the binomial distribution is

${\sigma{}}_{x}^{2}$ = npq

Step 2 of 3:

The claim is to find the probability that three or fewer of the winners will be women.

We have to find P(X $\leq{}$ 3) = P(x = 0) + P( x = 1) + P(x = 2) + P(x = 3)

P(x: n,p) = ${(}_{x}^{n})$ ${p}^{x}$ (1 - p ${)}^{(n-x)}$ , x = 0, 1, 2, ….., n.

Where, n = 5, p = 0.6 and x = 0, 1, 2 and 3.

P(X $\leq{}$ 3) = ${(}_{0}^{5})$ ${(0.60)}^{0}$ (1 - 0.60 ${)}^{(5-0)}$ + ${(}_{1}^{5})$ ${(0.60)}^{1}$ (1 - 0.60 ${)}^{(5-1)}$ +

${(}_{2}^{5})$ ${(0.60)}^{2}$ (1 - 0.60 ${)}^{(5-2)}$ + ${(}_{3}^{5})$ ${(0.60)}^{3}$ (1 - 0.60 ${)}^{(5-3)}$

= (1) (1) (0.01024) + (5) (0.60) (0.0256) +

(10) (0.36) (0.064) + (10) (0.216) (0.16)

= 0.01024 + 0.0768 + 0.2304 + 0.3456

= 0.66304

Hence, the probability that three or fewer of the winners will be women is 0.66304

Step 3 of 3

Chapter 4.2, Problem 9E is Solved

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

This full solution covers the following key subjects: tickets, winners, Gender, Women, Probability. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 9E from 4.2 chapter was answered, more than 489 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “Several million lottery tickets are sold, and 60% of the Tickets are held by women. Five winning tickets will be drawn at random.a. What is the probability that three or fewer of the winners will be women?________________b. What is the probability that three of the winners will be of one gender and two of the winners will be of the other gender?” is broken down into a number of easy to follow steps, and 62 words. The full step-by-step solution to problem: 9E from chapter: 4.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.