Question

2. Use the SAS profit function to find the following percentiles for a normal random variable with mean 500 and standard deviation 100.

a. 5th percentile

b. 50th percentile

c. 80th percentile

d. 95th percentile

Answer 1

Solution :

mean = = 500

standard deviation = = 100

a. Using standard normal table,

P(Z < z) = 5%

P(Z < z) = 0.05

P(Z < -1.65) = 0.05

z = -1.65

Using z-score formula,

x = z * +

x = -1.65 * 100 + 500

x = 335

5th percentile = 335

b. Using standard normal table,

(Z < z) = 50%

P(Z < z) = 0.5

P(Z < 0) = 0.5

z = 0

Using z-score formula,

x = z * +

x = 0 * 100 + 500

x = 500

50th percentile = 500

c. Using standard normal table,

P(Z < z) = 80%

P(Z < z) = 0.8

P(Z < 0.84) = 0.8

z = 0.84

Using z-score formula,

x = z * +

x = 0.84 * 100 +500

x = 584

80th percentile = 584

d. Using standard normal table,

(Z < z) = 95%

P(Z < z) = 0.95

P(Z < 1.65) = 0.95

z = 1.65

Using z-score formula,

x = z * +

x = 1.65 * 100 + 500

x = 665

95th percentile = 665