Question

(1 point) Consider a normal distribution curve where 90-th percentile is at 11 and the 25-th percentile is at 9. Use this information to find the mean, μ , and the standard deviation, σ , of the distribution.

a) ?= 9.6873 (right answer)

b) σ = 1.025 (not correct?) I have tried this answer but webwork will not accept it. Is there possibly another answer

Answer 1

Solution:

The critical Z value for 90^th percentile by using z-table is given as Z = 1.28

The critical Z value for 25^th percentile by using z-table is given as Z = -0.68

X = µ + Z*σ

So, from given information, we have

µ + 1.28*σ = 11 ...........(1)

µ - 0.68*σ = 9 ..............(2)

Subtract equation 2 from equation 1, we get

1.96*σ = 11 - 9 = 2

σ = 2/1.96

σ = 1.02041

µ + 1.28*σ = 11

µ + 1.28*1.02041 = 11

µ + 1.30612 = 11

µ = 11 - 1.30612

µ = 9.69388

a) μ=9.69388

b) σ= 1.02041

Try these answers still it shows incorrect please post a comment i will try to correct the answers. thank you