Question

A set of data items is normally distributed with a mean of 15 and a standard deviation of 7.3. Find the data value in the distribution that corresponds to each of the following z-scores. Round your answers to the nearest tenth.

(a) z = -1.05



(b) z = 2.72

Answer 1

it is given that and

(A) we have to find the x value corresponding to z value of -1.05

using the formula z = (x-mean)/(standard deviation)

setting the given values, we get

-1.05 = (x-15)/7.3

by cross multiplication, we get

-1.05*7.3 = x - 15

-7.665 = x -15

adding 15 on each side, we get

-7.665 + 15 = x -15 + 15

this gives x value = 7.335 or 7.3(rounded to nearest tenth decimals)

(B) we have to find the x value corresponding to z value of 2.72

using the formula z = (x-mean)/(standard deviation)

setting the given values, we get

2.72 = (x-15)/7.3

by cross multiplication, we get

2.72*7.3 = x - 15

19.856 = x -15

adding 15 on each side, we get

19.856+ 15 = x -15 + 15

this gives x value = 34.856 or 34.9 (rounded to 3 decimals)