Question

Consider a normal distribution curve where 90-th percentile is at 17 and the 40-th percentile is at 8. Use this information to find the mean, μ , and the standard deviation, σ , of the distribution.

a) μ=

b) σ=

Answer 1

Solution:

The critical Z value for 90^th percentile by using z-table is given as Z = 1.281552

The critical Z value for 40^th percentile by using z-table is given as Z = -0.25335

X = µ + Z*σ

So, from given information, we have

µ + 1.281552*σ = 17

µ - 0.25335*σ = 8

Subtract equation 2 from equation 1, we get

1.534899*σ = 17 - 8 = 9

σ = 9/1.534899

σ = 5.863578

µ + 1.281552*σ = 17

µ + 1.281552*5.863578 = 17

µ + 7.51448 = 17

µ = 17 - 7.51448

µ = 9.48552

a) μ=9.48552

b) σ= 5.863578