Chapter 3.1, Problem 3.18E

(a)

To determine

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

Answer to Problem 3.18E

Mean = 162.5

Standard deviation = 6.5

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 16 years old female height is 162.5 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 169

  $\begin{array}{l}\text{z}\text{score at z = 1 is 169,}\\ \overline{x}+1\sigma =169\\ 162.5+\sigma =169\\ \sigma =169-162.5\\ \sigma =6.5\end{array}$

(b)

To determine

To calculate the value of height of female with age 16 years at z = -1.5.

Answer to Problem 3.18E

Value of height at z = 152.75

Explanation of Solution

Calculation:

The value of height at z = -1.5:

  $\begin{array}{l}\overline{x}-1.5\sigma \\ =162.5-1.5\times 6.5\\ =152.75\end{array}$