Chapter 2, Problem T2.7SPT

To determine

To find: the standard deviation of the heights in this population.

Answer to Problem T2.7SPT

  $\sigma =4\text{'}\text{'}$

Explanation of Solution

Given:

99.7% of the height is between 5’0’’ and 7’0’’

Calculation:

Rule for the normal distribution that 99.7% of data would be lie within 3 standard deviation of the mean.

Mean lies in the middle of the interval and therefore is at 6’0’’.

And knowing that 3 standard deviation is between 5’0’’ and 6’0’’

  $3\sigma =1\text{'}0\text{'}\text{'}=12\text{'}\text{'}$

Dividing each side by 3:

  $\sigma =\frac{12\text{'}\text{'}}{3}=4\text{'}\text{'}$

Graph:

  

Hence, the correct option is (c)