Chapter 6.1, Problem 19E

a.

To determine

To construct: The histogram to make the comparison of X and Y. Also, discuss the difference that could be observed in these two distributions.

Explanation of Solution

Given:

The probability distributions are:

	1	2	3	4	5	6	7	8	9	10
Owned	0.003	0.002	0.023	0.104	0.21	0.224	0.197	0.149	0.053	0.035
Rented	0.008	0.027	0.287	0.363	0.164	0.093	0.039	0.013	0.003	0.003

Formula used:

The formulas to compute the mean and standard deviation are:

  $\text{Mean =}{\displaystyle \sum x\times P\left(x\right)}$

  $\sigma \text{=}\sqrt{{\displaystyle \sum x^2\times P\left(x\right)}-{\left({\displaystyle \sum x\times P\left(x\right)}\right)}^2}$

Graph:

The histograms could be constructed as:

  

  

Interpretation:

By looking at the above graph it could be said that there are more rooms for the owners that the renters. On the other hand, the distribution for owned is ball shaped which implies that it is approximately normally distributed.

b.

To determine

To find: The mean for both the distribution and compare them.

Explanation of Solution

Calculation:

The mean for both the distributions using Ti-83 plus calculator could be calculated as:

For owned:

  

For rented:

  

Thus, the mean is 6.280 and 4.187 respectively.

There is a difference in two means because of the type of distributions.

c.

To determine

To find: The standard deviations for both the distributions.

Explanation of Solution

From above part, it is known that the standard deviations of owned and rented distributions are 1.63 and 1.31 respectively