Chapter 2.1, Problem 26E

(a)

To determine

Shape of the resulting distribution.

Answer to Problem 26E

The distribution is skewed to right with a single peak.

Explanation of Solution

Given information:

  $12\text{in}\text{.}=1\text{ft}\text{.}$

In order to convert the distances from inches to feet, every distance value in inches needs to be divided by 12.

In the previous problem,

We came to know that the shape of the distribution of distances was skewed to right along with a single peak.

When every value in the data is divided by 12, then the shape of the distribution will not be affected because there will be no change in the relationships between every data pair.

Thus,

The shape of the distribution of distances in this case is also skewed to right along with a single peak.

(b)

To determine

Mean of the distribution of distance in feet.

Answer to Problem 26E

Mean of the distribution of distance is 6.083 feet.

Explanation of Solution

Given information:

  $12\text{in}\text{.}=1\text{ft}\text{.}$

Mean, $\overline{\text{x}}=73\text{in}\text{.}$

In order to convert the distances from inches to feet, every distance value in inches needs to be divided by 12.

When we divide every data value by 12, then the center of the distribution also to be divided by 12, because the mean is the measure of the center.

In the previous problem,

We came to know that the mean of the distribution of the distance was 73 inches. For converting the mean of the distribution of distances from inches to feet, we need to divide the mean in inches by 12.

  $\overline{\text{x}}=\frac{73}{12}=6.083\text{ft}\text{.}$

Thus,

The mean of the distribution of distance in feet is 6.083 feet.

(c)

To determine

Standard deviation of the distribution of distance in feet.

Answer to Problem 26E

Standard deviation of the distribution of the distance is 0.3575 feet.

Explanation of Solution

Given information:

  $12\text{in}\text{.}=1\text{ft}\text{.}$

Standard deviation, $s_x=4.29\text{in}\text{.}$

In order to convert the distances from inches to feet, every distance value in inches needs to be divided by 12.

In the previous problem,

We came to know that the standard deviation of the distribution of the distance was 4.29 inches. For converting the standard deviation of the distribution of distances from inches to feet, we need to divide the standard deviation in inches by 12.

  $s_x=\frac{4.29}{12}=0.3575\text{ft}\text{.}$

Thus,

The standard deviation of the distribution of distance in feet is 0.3575 feet.