Question

A minimum height is to be prescribed for eligibility to
government services such that 75.80% of the young men will have a
fair chance of coming up to that standard. The height of young
men is normally distributed with mean 62 inches and standard
deviation 3.5 inches. Determine the minimum specification.

Answer 1

$Given \; that, μ=62, σ=3.5,\\ Let\; Z_{1}=\frac{X-62}{3.5}, then\\ P(Z>Z_{1})=0.758\\ 0.5+P(-Z_{1}<Z<0)=0.758\\ P(-Z_{1}<Z<0)=0.258\\ -Z_{1}=0.7 \implies Z_{1}=-0.7\\ \therefore -0.7=\frac{X-62}{3.5}\\ X=(-0.7\times 3.5)+62=59.55\\ \text{the minimum specification is}\;59.55\; inches$