Chapter PI, Problem 32RE

(a)

To determine

To describe the shape, centre and spread of this distribution.

Explanation of Solution

In the question it is given that horse power is another measure commonly used to describe auto engines. The summary statistics and the histogram displaying horse powers of the cars is also given. Thus, we can say by looking at the histogram is that the graph is roughly bimodal but does not have definitive modes. And the centre is about at $90$ . The graph seems to be slightly skewed to the right.

(b)

To determine

To find out what is the interquartile range.

Answer to Problem 32RE

  $47$ .

Explanation of Solution

In the question it is given that horse power is another measure commonly used to describe auto engines. The summary statistics and the histogram displaying horse powers of the cars is also given. Thus, the interquartile range is calculated by the taking the difference between third quartile and the first quartile so, we have,

  $\begin{array}{l}=125-78\\ =47\end{array}$

(c)

To determine

To explain are any of these engines outliers in terms of horse power.

Answer to Problem 32RE

No, there are not any.

Explanation of Solution

In the question it is given that horse power is another measure commonly used to describe auto engines. The summary statistics and the histogram displaying horse powers of the cars is also given. Thus, we can say that there are not any of these engines outliers in terms of horse power because none of the values are very far from the IQR or very lower.

(d)

To determine

To explain do you think the $68-95-99.7$ rule applies to the horse power of auto engines.

Answer to Problem 32RE

No, we cannot apply.

Explanation of Solution

In the question it is given that horse power is another measure commonly used to describe auto engines. The summary statistics and the histogram displaying horse powers of the cars is also given. Thus, we cannot use the $68-95-99.7$ rule to apply to the horse power of auto engines because the histogram is not uni-modal, it is bimodal.

(e)

To determine

To estimate the percentage of these engines whose horse power is within one standard deviation of the mean.

Answer to Problem 32RE

  $75\%$ .

Explanation of Solution

In the question it is given that horse power is another measure commonly used to describe auto engines. The summary statistics and the histogram displaying horse powers of the cars is also given. Thus, the estimated percentage of these engines whose horse power is within one standard deviation of the mean is that

  $\begin{array}{l}101.7-26.4\\ =75.3\\ 101.7+26.4\\ =128.1\end{array}$

Son from $75.3\text{ to 128}\text{.1}$ about $75\%$ will be the estimate percentage of the mean.

(f)

To determine

To explain what would happen to each of these summary statistics if this additive were used in all cars.

Explanation of Solution

In the question it is given that horse power is another measure commonly used to describe auto engines. The summary statistics and the histogram displaying horse powers of the cars is also given. Thus, this would happen to each of these summary statistics if this additive were used in all cars because the count would not change. The mean would increase by ten and the median would increase by ten and the standard deviation would remain the same.