Question

Suppose you are working with a data set that is normally distributed, with a mean of 100 and a standard deviation of 42. Determine the value of x from the following information. (Round your answers and z values to 2 decimal places.)

(a) 80% of the values are greater than x.

(b) x is less than 14% of the values.

(c) 23% of the values are less than x.

(d) x is greater than 52% of the values.

Answer 1

Solution:

We are given

µ = 100

σ = 42

x = µ + Z*σ

Part a

Z value for upper 80% area by using z-table or excel is given as below:

Z = -0.84162

x = µ + Z*σ

x = 100 + (-0.84162)*42

x = 64.65

Part b

Z value for the upper 14% area by using z-table or excel is given as below:

Z = 1.080319

x = µ + Z*σ

x = 100 + 1.080319*42

x = 145.37

Part c

Z value for lower 23% area by using z-table or excel is given as below:

Z = -0.73885

x = µ + Z*σ

x = 100 + (-0.73885)*42

x = 68.97

Part d

Z value for lower 52% area by using z-table or excel is given as below:

Z = 0.050154

x = µ + Z*σ

x = 100 + 0.050154*42

x = 102.11