Question

A set of data items is normally distributed with a mean of 30 and a standard deviation of 6.4. Find the data value in the distribution that corresponds to each of the following z-scores. Round your answers to the nearest tenth (one decimal place).

Z=-1.5

Answer: ____

Z= 1.6

Answer:_____

Answer 1

Solution.

Given that,

$\mu$ = 30

$\sigma$ = 6.4

a.Given that

z = -1.5

Using z score formula,

x = z $\sigma$ + $\mu$

x = -1.5 × 6.4 + 30 = 20.4

Data value is 20.4

b.Given that

z = 1.6

Using z score formula,

x = z $\sigma$ + $\mu$

x = 1.6 × 6.4 + 30 = 40.2

Data value 40.2