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Solved: In Exercises, assume that 40% of the population

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 2RE Chapter 5.5

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 2RE

Problem 2RE

In Exercises, assume that 40% of the population has brown eyes (based on data from Dr. P. Sorita at Indiana University).

Brown Eyes Find the probability that among six randomly selected people, exactly four of them have brown eyes.

Step-by-Step Solution:
Step 1 of 3

Problem 2RE

Answer:

Step1 of 1:

We have In Exercises, assume that 40% of the population has brown eyes (based on data from Dr. P. Sorita at Indiana University) that is p = 40% = 0.40.we need to find the probability that among six randomly selected people, exactly four of them have brown eyes.

Here,

P = 0.40 n = 6

Consider a random variable “x” follows binomial distribution with sample size “n” and proportion “p”.

i,e.X B(n, p)

Where,

n = 6 and p = 0.40.

q = 1 - p

   = 1 - 0.40

   = 0.6.

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

Now,

The probability that among six randomly selected people, exactly four of them have brown eyes is given by

      P(x) =

P(x = 4) =

              =  150.02560.36

              = 0.1382.

Step 2 of 3

Chapter 5.5, Problem 2RE is Solved
Step 3 of 3

Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

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Solved: In Exercises, assume that 40% of the population