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Chapter 4: Q. 4.12 (page 256)

Sixty-five percent of people pass the state driver鈥檚 exam on the first try. A group of 50individuals who have taken the driver鈥檚 exam is randomly selected. Give two reasons why this is a binomial problem.

Short Answer

Expert verified

The two reasons are:

  1. In binomial problem, there must be an infinite number of nof independent trials and after each trial the outcome may be success or failure.
  2. The probability of pass in each state driver's exam in the first try is constant p=0.65,then the probability of fail in each state driver's exam in the first try q=0.35

Step by step solution

01

Content Introduction

We are given

65%of people pass the state driver鈥檚 exam on the first try.

A group of 50individuals who have taken the driver鈥檚 exam is randomly selected.

We need to state the two reason that the given information is about binomial problem.

02

Content Explanation

The two reasons why the given problem is a binomial problem are:

  1. In binomial problem, there must be an infinite number of nof independent trials and after each trial the outcome may be success or failure. There are n=50individuals who took drivers exam where, individuals were randomly selected and the outcome was either pass or fail. Also, individual exam is independent to each other.
  2. Another, is that the probability of success pis constant at each trial. Therefore, the probability of pass in each state driver's exam in the first try is constant p=65%or0.65. then the probability of fail in each state driver's exam in the first try is 100%-65%=35%or0.35. Also, if interested in the outcome success that is pass, then we define the random variable as X=number of individuals pass the state driver鈥檚 exam out of 50individuals.

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