Question

A study was done on heights of giraffes where it was found thatthe mean was around 15 feet tall with a standard deviation of 2ft. According to this study, what percent of giraffes are between11 and 19 feet tall?

Answer 1

Note that the proportion, percentage, and probability are equivalent. So we can use the concept of probability to obtain the percentage.

Since the mean and standard deviation are known, and the height is a continuous variable, the problem can be answered using Normal Probability Distribution.

Let X be the random variable representing the height of giraffes.

The mean and standard deviation are given as 15 and 2 ft.,

`\begin{gathered} \mu=15 \\ \sigma=2 \end{gathered}`

Consider that the z-score corresponding to any value of 'x' is given by,

`z=(x-\mu)/(\sigma)`

Then the probability that the height lies between 11 and 19 feet, is calculated as,

Substitute the value,

[tex]\begin{gathered} P(11Thus, approximately 95.44% percentage of giraffes are between 11 and 19 feet tall.