Chapter 3.1, Problem 3.17E

(a)

To determine

To calculate the mean and standard deviation using the given z scores for 15 years.

Answer to Problem 3.17E

Mean = 170

Standard deviation = 7.5

Explanation of Solution

Given:

  $\begin{array}{l}\text{For 15 year old Males}\\ \text{Z score = 0 at 170 cms}\text{.}\\ \text{Z score = 1 at 177}\text{.5 cms}\text{.}\end{array}$

  $\begin{array}{l}\text{For 16 year old females}\\ \text{Z score = 0 at 162}\text{.5 cms}\text{.}\\ \text{Z score = 1 at 169 cms}\text{.}\end{array}$

The value of 15 years old male height is 170 and the value at z score equal 0 is always equal to mean when the data follows normal distribution.

The standard deviation:

The value of height at z = 1 is 177.5

  $\begin{array}{l}\text{z}\text{score at z = 1 is 177}\text{.5,}\\ \overline{x}+1\sigma =177.5\\ 170+\sigma =177.5\\ \sigma =177.5-170\\ \sigma =7.5\end{array}$

(b)

To determine

To calculate the value of height of male at z = 2.5.

Answer to Problem 3.17E

Value of height at z = 188.75

Explanation of Solution

Calculation:

The value of height at z = 2.5:

  $\begin{array}{l}\overline{x}+2.5\sigma \\ =170+2.5\times 7.5\\ =188.75\end{array}$