Question

Normal distribution. mean 20, standard deviation 5
P(20-k < X < 20+k)=0.8684 Find k

Answer 1

The cumulative probability that all data points are below 20 + k is given by
\[0.5000+\frac{0.8684}{2}=0.9342\]
The z-score corresponding to a cumulative probability of 0.9342 is 1.51.

Using the formula
\[z=\frac{X-\mu}{\sigma}\]
\[1.51=\frac{X-20}{5}\ .............(1)\]
Now solve equation (1) to find the value of X. Then plug the value of X into the following equation to find k.
k = X - 20