Chapter 6, Problem 12PT

a.

To determine

To explain: The random variable X being binomial random variable.

Explanation of Solution

Given:

Probability of success ( p ) = 66% = 0.66

Number of trials ( n ) = 12

The random variable X being binomial random variable:

1. There are two successes and failures, that is, greet dog and do not greet dog.
2. Dogs are independent of each other.
3. Number of dog owners are fixed.
4. Probability of success is fixed.

Since, all the required condition for a binomial distribution are fixed. Thus, the variable X is a binomial random variable.

b.

To determine

To find: The probability only 4 dogs have been greeted first. Also, find whether the sufficient evidences have been provided the journal.

Explanation of Solution

Calculation:

The probability only 4 dogs have been greeted first can be computed as:

  

Thus, the required probability is 0.0213.

Here, probability is below 5%. Thus, there is sufficient evidence against the journal.