Chapter 6.2, Problem 37E

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:

X	0	1	2	3	4	5
Probability	0.02	0.05	0.08	0.16	0.27	0.42

Graph:

The figure could be constructed as:

  

Interpretation:

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

b.

To determine

To find: The ${\mu }_M$

Answer to Problem 37E

The mean of M is 19.35.

Explanation of Solution

Calculation:

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

  $\begin{array}{c}{\mu }_M=5\left(3.87\right)\\ =19.35\end{array}$

The average amount of collected on per trips is 19.35.

c.

To determine

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

Answer to Problem 37E

The standard deviation is 6.45.

Explanation of Solution

Calculation:

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

  $\begin{array}{c}{\sigma }_M=5\left(1.29\right)\\ =6.45\end{array}$

The amount that is collected by the ferry varies by $6.45 from the mean of $19.35.