Question

Suppose X is a normal random variable with mean μ = 70 and standard deviation σ = 4. Find b such that

P(70 ≤ X ≤ b) = 0.3.  (Round your answer to one decimal place.)

Answer 1

There are 50% data which is above mean.

Hence, 50% data above 70 but only 30% till 'b' so 'b' is 80th percetile.

For 80th percentile z = 0.8416 (from z-table)

x = mean + z*sd

b = 70 + 0.8416*4 = 73.3664

Hence, b = 73.4 (rounded to 1 decimal place).