Chapter 2.2, Problem 75E

To determine

Whether the distribution of refrigerator capacities approximately normal.

Answer to Problem 75E

The distribution of refrigerator capacities is approximately normal.

Explanation of Solution

Given information:

  

According to 68 − 95 − 99.7 rule:

68% of the data of a normal distribution lies with 1 standard deviation from the mean.

95% of the data of a normal distribution lies with 2 standard deviation from the mean.

99.7% of the data of a normal distribution lies with 1 standard deviation from the mean.

Then

The general Normal density graph is represented as:

  

Note that

The sample has 24 out of 36 observations within 1 standard deviation of the mean.

That means

The sample has 66.67% observations within 1 standard deviation.

Between

  $\overline{x}-s_x=15.825-1.217=14.608$

And

  $\overline{x}+s_x=15.825+1.217=17.042$

Also note that

The sample has 34 out of 36 observations within 2 standard deviation of the mean.

That means

The sample has 94.44% observations within 2 standard deviation.

Between

  $\overline{x}-2s_x=15.825-2\left(1.217\right)=13.391$

And

  $\overline{x}+2s_x=15.825+2\left(1.217\right)=18.259$

Also note that

The sample has 36 out of 36 observations within 3 standard deviation of the mean.

That means

The sample has 100% observations within 3 standard deviation.

Between

  $\overline{x}-3s_x=15.825-3\left(1.217\right)=12.174$

And

  $\overline{x}+3s_x=15.825+3\left(1.217\right)=19.476$

We have that

66.67% is very close to 68%.

94.44% is very close to 95%.

100% is very close to 99.7%.

This implies

The data reasonably follows 68 − 95 − 99.7 rule.

Thus,

The distribution is approximately normal.