Chapter 6.1, Problem 9E

(a)

To determine

To Explain: the shape of given histogram

Answer to Problem 9E

Skewed to the right or Positive skewed

Explanation of Solution

The distribution is skewed to the right, because the tail of smaller bar is to the right in the histogram and highest bar in the histogram is to the left.

(b)

To determine

To Calculate: the expected value of X

Answer to Problem 9E

  ${\mu }_x=\text{E}\left(X\right)$ =3.441

Explanation of Solution

Given:

First Digit (X)	1	2	3	4	5	6	7	8	9
Probability	0.301	0.176	0.125	0.097	0.079	0.067	0.058	0.051	0.046

Formula used:

  ${\mu }_x=\text{E}\left(X\right)={\displaystyle \sum {\text{P}}_i}{X}_i$

Calculation:

First digit (X)	Probability(P(X))	$\text{XP}\left(X\right)$
1	0.301	0.301
2	0.176	0.352
3	0.125	0.375
4	0.097	0.388
5	0.079	0.395
6	0.067	0.402
7	0.058	0.406
8	0.051	0.408
9	0.046	0.414
		3.441

  ${\mu }_x=\text{E}\left(X\right)$ =3.441

The average of first digit will be 3.441