Chapter 10.2, Problem 10.35E

(a)

To determine

To construct: a histogram of these 50 observations and explain about the shape.

Explanation of Solution

Given:

  

Calculation:

Table on the basis of given data of interval and frequency

Interval	Frequency
0.425-0.45	5
0.45-0.475	8
0.475-0.5	17
0.5-0.525	6
0.525-0.55	13
0.55-0.575	1

Graph:

Bar graph

  

By seeing that the width of the bars have to be the same and the bars have to be bounded horizontally by the interval limits. The height of the bars has to be equal the frequency.

(b)

To determine

To construct: a graph of the density curve for the population distribution and the value of the population mean.

Explanation of Solution

The histogram looking roughly Normal, because the one of highest bar is in the middle of the histogram and the histogram does not displaying any strong skewed

Graph:

Bar graph

  

When we randomly select a number between 0and 1, then we have a uniform distribution on (0, 1).

The mean of the uniform distribution

  $\mu =\frac{0+1}{2}=\frac{1}{2}=0.5$