Question

The heights of a group of trees is normally distributed with a mean of 14.3 feet. If the z score for a 20-foot y’all tree is 1.9, what is the standard deviation?

Answer 1

The standard deviation of the heights of the group of trees is 3 feet

Explanation:

For a normal distribution, the z-score corresponding to a particular observed value is calculated as;

z-score = (observed value - mean) / (standard deviation)

The mean is given as 14.3

The z-score is 1.9

The observed value is 20 (the given height)

We can make the standard deviation to be the subject of the formula in the above equation;

standard deviation = (observed value - mean) / ( z-score)

We then substitute the given values into this equation;

standard deviation =
`(20-14.3)/(1.9)=3`