Chapter 6, Problem 5CRE

a.

To determine

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

Explanation of Solution

Given:

Probability of success ( p ) = 20% = 0.20.

Number of trials ( n ) = 8

The random variable X being binomial random variable:

1. There are two successes and failures, that is, candy is orange and candy is not orange
2. Candies are independent of each other.
3. Number of candies are fixed.
4. Probability of getting orange candy 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 mean and interpret it.

Answer to Problem 5CRE

The mean is 1.60.

Explanation of Solution

Calculation:

The mean can be calculated as:

  $\begin{array}{c}\mu =n\times p\\ =8\left(0.20\right)\\ =1.60\end{array}$

The above computed mean shows that the expected number of candies is 1.

c.

To determine

To find: The standard deviation and interpret it.

Answer to Problem 5CRE

The standard deviation is 1.1314.

Explanation of Solution

Calculation:

The standard deviation can be calculated as:

  $\begin{array}{c}\sigma =\sqrt{n\times p\times \left(1-p\right)}\\ =\sqrt{8\left(0.20\right)\left(1-0.20\right)}\\ =1.1314\end{array}$

The above computed mean shows that the number of the candies will differ by 1.1314 by the average of 1.60 candies.