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Voters. In Exercises, use a normal approximation to find

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

Solution for problem 10BSC Chapter 6.7

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 10BSC

Voters. In Exercises, use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 18–24 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 18–24, 22% of them voted.

Probability that at least 25 voted

Step-by-Step Solution:
Step 1 of 3

Problem 10BSC

Answer:

Step1 of 4:

We have 100 eligible voters aged 18–24 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 18–24, 22% of them voted.

Step2 of 4:

We need to find the probability of the indicated number of voters.

Step3 of 4:

We have n = 100, p = 22% = 0.22 and

q = 1 - p

   = 1 - 0.22

   = 0.78

Let “x” be random variable it follows binomial distribution with parameter n and p.

x B(n, p)

1).Mean of the binomial distribution is given by () = np

                                                                                     = 100(0.22)

                                                                                     = 22

                                                           

2).Variance of the binomial distribution is given by () =  npq

                                                                                            = 100(0.22)(0.78)

                                                                                            = 17.16

3).standard deviation of the binomial distribution is given by () =

                                                                                                                            

                                                                                                          =                

                                                                                                          = 4.1424

Step4 of 4:

Consider z statistics with x = 25.5

P() = 1 - P(z )

                            = 1 - P(z )

                            = 1 - P(z0.8449)

                            = 1 - 0.7995

                               = 0.2005.

Probability that 0.8449 is calculated by using standard normal table(area under normal curve).in statistical table we have to see row 0.8 under column 0.04

Hence, P(z < 0.8449) = 0.7995

Conclusion:

Therefore,Probability that at least 25 voted is 0.2005.

 

 

Step 2 of 3

Chapter 6.7, Problem 10BSC is Solved
Step 3 of 3

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

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Voters. In Exercises, use a normal approximation to find