One out of every 5000 individuals in a population carries

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

ISBN: 9780073401331 38

Solution for problem 6E Chapter 4.3

Statistics for Engineers and Scientists | 4th Edition

Textbook Solutions
2901 Step-by-step solutions solved by professors and subject experts
Get 24/7 help from StudySoup virtual teaching assistants

Statistics for Engineers and Scientists | 4th Edition

4 5 1 396 Reviews

Problem 6E

One out of every 5000 individuals in a population carries a certain defective gene. A random sample of 1000 individuals is studied.

a. What is the probability that exactly one of the sample individuals carries the gene?

b. What is the probability that none of the sample individuals carries the gene?

c. What is the probability that more than two of the sample individuals carry the gene?

d. What is the mean of the number of sample individuals that carry the gene?

e. What is the standard deviation of the number of sample individuals that carry the gene?

Step-by-Step Solution:

Solution

Step 1 of 6

Here given one out of every 5000 individual in a population carries a certain defective gene

So, p=1/5000

=0.0002

The sample size 1000

So, n=1000

Let X is no.of individuals carries the gene

Here X $\sim{}$ B(1000,0.0002)

Since ‘n’ is large and ‘p’ is small

The Binomial distribution will be converted to poisson distribution

The pmf of poisson distribution is P(X)= $\frac{e{\ }^{-\lambda{}}\lambda{}{\ }^{x}}{x!}$ , X=0,1,2,..............

So, $\lambda{}$ =np

=1000(0.0002)

=0.2

Hence X $\sim{}$ Poisson (0.2)

Step 2 of 6

Chapter 4.3, Problem 6E is Solved

Step 3 of 6

Textbook: Statistics for Engineers and Scientists

Edition: 4

Author: William Navidi

ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: Individuals, gene, sample, Probability, carry. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 6E from chapter: 4.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “?One out of every 5000 individuals in a population carries a certain defective gene. A random sample of 1000 individuals is studied.a. What is the probability that exactly one of the sample individuals carries the gene?b. What is the probability that none of the sample individuals carries the gene?c. What is the probability that more than two of the sample individuals carry the gene?d. What is the mean of the number of sample individuals that carry the gene?e. What is the standard deviation of the number of sample individuals that carry the gene?” is broken down into a number of easy to follow steps, and 93 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 6E from 4.3 chapter was answered, more than 1518 students have viewed the full step-by-step answer.