Chapter 2, Problem R2.1RE

(a)

To determine

To Calculate: the z-score and the value means.

Answer to Problem R2.1RE

  $z=1.20$

Explanation of Solution

Given:

  $\begin{array}{l}x\text{=179}\text{cm}\\ \mu \text{=170}\text{cm}\\ \sigma \text{=7}\text{.5}\text{cm}\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ z=\frac{179-170}{7.5}\\ z=1.20\end{array}$

It means that researcher’s means height is 170 cm which is about to the standard deviation 1.20. Height of the researcher’s would be between 168.8 cm and 171.2 cm.

(b)

To determine

To Explain: that this means to someone who knows no statistics.

Explanation of Solution

85^th percentile is data point where 85% of the entire data is less than or equal to the data point. It also means that 15% of the data is greater than or equal to the data point so researcher is taller than 85% of the entire population of 15-year old males or shorter than 15% of the entire population of 15-years old males.