Question

Please

Weights of male mountain lions follow the normal distribution with a median of 150 lb and an interquartile range of 8.2 lb.

Find the 75th percentile of the weights.

[Calculate your answer in pounds (lb), but do not enter the units of measurement.]

Answer 1

The standard deviation can be calculated using the formula
\[\sigma=\frac{Interquartile\ range}{1.34896}\]
In this case the standard deviation 8.2/1.34896= 6.079
A standard normal distribution table shows the z-score for a cumulative probability of 75% is
z = 0.675
The median and the mean are the same. Therefore the following formula can be used:
\[z=\frac{X-\mu}{\sigma}\]
Substituting we get
\[0.675=\frac{X-150}{6.079}\]
Solving for X gives
X = 150 + 4.1