Question

Consider a normal distribution curve where 80-th percentile is at 16 and the 45-th percentile is at 1. Use this information to find the mean,  μ , and the standard deviation, σ , of the distribution.

a) μ=  

b) σ=

Answer 1

here as we know that X =mean +z*sd deviation

for 80 th percentile ; z =0.8416

hence 16 =μ+0.8416*σ ..........(1)

for 45 th percentile: z =-0.1257

hence 1 =μ-0.1257*σ.............(2)

solving above

a)μ =2.95

b) σ= 15.51