Question

A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that corresponds to the given z-score. z = -3, if the standard deviation is 80.

Answer 1

260

Explanation:

The z score for a normal distribution is given by the formula

`z = (X-\mu)/(\sigma)`

where
X is the data point, μ is the mean and σ is the standard deviation

Given

Mean μ = 500
Standard deviation σ = 80
z-score = -3

and plugging in these values for z-score formula we get

`-3 = (X -500)/(80)`

==>
-240 = X - 500
-240 + 500 = X

260 = X

or

X = 260