Chapter 1, Problem 1.1E

Refer to the data and five-number summaries given in Case Study 1.1. Give a numerical value for each of the following.

1. The fastest speed driven by anyone in the class.
2. The slowest of the “fastest speeds” driven by a male.
3. The speed for which one-fourth of the women had driven at that speed or faster.
4. The proportion of females who had driven 89 mph or faster.
5. The number of females who had driven 89 mph or faster.

To determine

(a)

To find:

The fastest speed driven by a student in the class.

Answer to Problem 1.1E

  $\text{150 mph}$

Explanation of Solution

Given information:

The given data set:

  $\begin{array}{l}\boxed{\begin{array}{l}\text{Males: 110 109 90 140 105 150 120 110 110 90 115 95 145 140}\text{110 105 85 95 100 }\\ \text{115 124 95 100 125 140 85 120 115 105 125}\text{102 85 120 110 120 115 94 125 80 85 }\\ \text{140 120 92 130 125 110}\text{90 110 110 95 95 110 105 80 100 110 130 105 105 120 90 }\\ \text{100}\text{105 100 120 100 100 80 100 120 105 60 125 120 100 115 95}\text{110 101 80 112 }\\ \text{120 110 115 125 55 90}\end{array}}\\ \boxed{\begin{array}{l}\text{Females: 80 75 83 80 100 100 90 75 95 85 90 85 90 90 120 85}\text{100 120 75 85 80 70 }\\ \text{85 110 85 75 105 95 75 70 90 70 82 85}\text{100 90 75 90 110 80 80 110 110 95 75 130 }\\ \text{95 110 110 80 90}\text{105 90 110 75 100 90 110 85 90 80 80 85 50 80 100 80 80 80}\text{95 }\\ \text{100 90 100 95 80 80 50 88 90 90 85 70 90 30 85 85 87 85}\text{90 85 75 90 102 80 100 }\\ \text{95 110 80 95 90 80 90}\end{array}}\end{array}$

Five number summary of the above data is given below.

  $\boxed{\begin{array}{ccc}\begin{array}{c}\begin{array}{l}\\ \end{array}\\ \text{Median }\\ \text{Quartiles }\\ \text{Extremes }\end{array}& \begin{array}{c}\begin{array}{l}\text{ Males}\\ \text{(87 Students)}\end{array}\\ 110\\ \begin{array}{cc}95& 120\end{array}\\ \begin{array}{cc}55& 150\end{array}\end{array}& \begin{array}{c}\begin{array}{l}\text{ Females }\\ \text{(102 Students)}\end{array}\\ 89\\ \begin{array}{cc}80& 95\end{array}\\ \begin{array}{cc}30& 130\end{array}\end{array}\end{array}}$

From the five-number summary table extreme values, it can be concluded that the highest speed of males is $\text{150 mph}$ and the highest speed of females is $\text{130 mph}$.

Hence, the fastest speed driven is $\text{150 mph}$.

To determine

(b)

To find:

The minimum speed of the "fastest speeds" driven by a male.

Answer to Problem 1.1E

  $\text{55 mph}$

Explanation of Solution

The five number summary table extreme values of males show that the minimum speed of a male is $\text{55 mph}$.

Thus, the slowest of the "fastest speeds" driven by a male is $\text{55 mph}$.

To determine

(c)

To find:

The speed such that one $\text{-}$ fourth of the women had driven at that speed or faster.

Answer to Problem 1.1E

  $\text{95 mph}$

Explanation of Solution

One $\text{-}$ fourth of the women had driven at a speed or faster is the upper quartile of the data. From the five-number summary table, the cut $\text{-}$ off point for the upper quartile is $\text{95}$.

Hence, the one $\text{-}$ fourth of the women had driven at the speed of $\text{95 mph}$ or faster.

To determine

(d)

To find:

The proportion of women who had driven $89\text{ mph}$ or faster.

Answer to Problem 1.1E

  $0.5$

Explanation of Solution

In the five-number summary table, $89\text{ mph}$ is the median speed of females. It means that half of the females have driven at the speed of $89\text{ mph}$ or faster.

Hence, the proportion of females who had driven $89\text{ mph}$ or faster is $0.5$.

To determine

(e)

To find:

The number of women who had driven $89\text{ mph}$ or faster.

Answer to Problem 1.1E

  $51$

Explanation of Solution

In the above part it was calculated that the proportion of females who had driven $89\text{ mph}$ or faster is $0.5$.

The total number of female students is $102$.

Therefore, the number of females who had driven $89\text{ mph}$ or faster is,

  $0.5\times 102=51$