Question

Because P(z < .44) = .67, 67% of all z values are less than .44, and .44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does not appear in the z table, use the closest entry):

a. The 91st percentile (Hint: Look for area .9100.)

b. The 77th percentile

c. The 50th percentile

d. The 9th percentile

e. What is the relationship between the 70th z percentile and the 30th z percentile?

Answer 1

Solution:

For standard normal distribution

µ = 0
σ = 1

a)

The 91st percentile , Using table

91st percentile = 1.34

b)

The 77th percentile, Using table

77th percentile = 0.74

c)

The 50th percentile, Using table

50th percentile = 0.00

d)

The 50th percentile, Using table

9th percentile = -1.34

e. What is the relationship between the 70th z percentile and the 30th z percentile?

You can see in part a and d that for 91th percentile and 9th percentile values are 1.34 and -1.34. In similar way for 70th percentile and 30th percentile values would be -z and z

70th percentile = 0.52

30th percentile = -0.52