Question

Suppose X has a normal distribution with mean equal to 80 and standard deviation equal to 12.

Use Table 3 from the appendix (the normal distribution table) to calculate the 10th percentile, 20th percentile, 50th percentile, 80 percentile and 90th percentile of X.Percentile 10 20 50 80 90

Answer 1

Solution:-

Given that,

mean = = 80

standard deviation = = 12

1) 10 %

P(Z < z ) = 0.10

z =-1.28

Using z-score formula,

x = z * +

x = -1.28 * 12+80

x = 64.64

2)

20 %

P(Z < z) = 0.20

z =-0.84

Using z-score formula,

x = z * +

x = -0.84 * 12+80

x = 69.92

3)

50 %

P(Z < z) = 0.50

z =0

Using z-score formula,

x = z * +

x = 0 * 12+80

x = 80

4) 80 %

P(Z < z) = 0.80

z =0.84

Using z-score formula,

x = z * +

x = 0.84 * 12+80

x = 90.08

5)

90 %

P(Z < z) = 0.90

z =1.28

Using z-score formula,

x = z * +

x = 1.28* 12+80

x = 95.36