Question

Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z = − 1.6 z=-1.6 and z = 1.6 z=1.6 standard deviations of the mean (or within 1.6 standard deviations of the mean). What percent of the data points will fall in that range?

Answer 1

89.04% of the data points will fall in the given range of z = − 1.6 and z = 1.6

Explanation:

We are given a normally distributed data.

We have to find the percentage of data that lies within the range z = − 1.6 and z= 1.6

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

`P(-1.6 \leq z \leq 1.6)\\= P(z \leq 1.6) - P(z \leq -1.6)\\\text{Calculating the value from standard normal table}\\= 0.9452 - 0.0548 = 0.8904= 89.04\%`

89.04% of the data points will fall in the given range of z = − 1.6 and z= 1.6