Chapter 6.2, Problem 38E

a.

To determine

To construct: The graph for the provided probability distribution and comment on the shape.

Explanation of Solution

Given:

The probability distribution is:

Score	10	20	30	40	50
Probability	0.32	0.27	0.19	0.15	0.07

Graph:

The figure could be constructed as:

  

Interpretation:

The above constructed figure is skewed to the right because most of the data falling in the right side.

b.

To determine

To find: The ${\mu }_T$

Answer to Problem 38E

The mean of T is 2.38.

Explanation of Solution

Here, it is known that $T=\frac{X}{10}$

The value of the ${\mu }_T$ can be calculated as:

  $\begin{array}{c}{\mu }_T=\frac{1}{10}{\mu }_X\\ =\frac{1}{10}\left(23.8\right)\\ =2.38\end{array}$

The average number of tickets are 2.38.

c.

To determine

To find: The ${\sigma }_T$ and interpret it.

Answer to Problem 38E

The standard deviation of T is 1.263.

Explanation of Solution

The value of the ${\sigma }_T$ can be calculated as:

  $\begin{array}{c}{\sigma }_T=\frac{1}{10}\times {\sigma }_X\\ =\frac{1}{10}\times \left(12.63\right)\\ =1.263\end{array}$

The total number of tickets are varying about 1.263 from the mean of total 2.38 tickets.