Question

Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between
z
=
−
1.5
and
z
=
1.5
standard deviations of the mean (or within 1.5 standard deviations of the mean). What percent of the data points will fall in that range?

Answer 1

Answer:

86.64% of the data points will fall in that range

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem:

z = -1.5 has a pvalue of 0.0668

z = 1.5 has a pvalue of 0.9332

0.9332 - 0.0668 = 0.8664

86.64% of the data points will fall in that range