Question

A variable x is normally distributed with mean 17 and standard deviation 6. Round your answers to the nearest hundredth as needed.

a) Determine the z -score for x = 19 .

z =

b) Determine the z -score for x = 13 .

z =

c) What value of x has a z -score of 2 ?

x =

d) What value of x has a z -score of − 0.3 ?

x =

Answer 1

Solution :

Given that ,

mean = = 17

standard deviation = = 6

a)

x = 19

z = (x - ) /

= ( 19 - 17 ) / 6

= 2 / 6

= 0.33

The z-score is 0.33

b)

x = 13

z = (x - ) /

= ( 13 - 17 ) / 6

= -4 / 6

= -0.67

The z-score is -0.67

c)

z = 2

Using z-score formula,

x = z* +

= 2*6 + 17

= 29

value of x has 29

d)

z = -0.3

Using z-score formula,

x = z* +

= -0.3*6 + 17

= 15.20

value of x has 15.20