Chapter 6.3, Problem 93E

To determine

To construct: The graph for the probability distribution of X and describe its shape.

Explanation of Solution

Given:

Probability of success ( p ) = 0.80

Number of trials ( n ) = 12

Calculation:

Consider, X be the random variable that represents the number of times spinner lands in the blue region follows the binomial distribution with parameters n = 12 and p = 0.80.

The probability distribution can be written as:

  $P\left(X=r\right){=}^{12}{C}_r\times {\left(0.80\right)}^r\times {\left(1-0.80\right)}^{12-r}$

Graph:

The figure for the probability distribution of X can be constructed as:

  

From the above figure, it can be observed that the left tail of the graph is much longer than the right tail, thus the distribution is skewed to the left.