Question

The weights of adult men in a hypothetical population are approximately normally distributed about a mean of 175 lbs. with a standard deviation of 15 lbs. If Harvey is at the 95th percentile in height for adult men, his weight, in pounds, is closest to:

Answer 1

First find the z-score corresponding to a cumulative probability of 0.95. Reference to a standard normal distribution table gives z = 1.645.
Next we use the equation
\[z=\frac{X-\mu}{\sigma}\]
and plug in the known values of z, mu and sigma giving:
\[1.645=\frac{X-175}{15}\ ..............(1)\]
By rearranging (1) we can find the required value of X as follows:
\[X=175+(15 \times 1.1.645)=you\ can\ calculate\]