Indicated Probability

Question

Assume the random variable x is normally distributed with mean μ=87 and standard deviation σ=5.

Find the indicated probability.

​P(72<x<83​)

Answer 1

For mean 87 and SD = 5, z = (x - 87)/5

Transform P(72 < x < 83) to P( (72-87)/5 < z < (83 - 87)/5) = P(-3 < z < -0.8) = P(z < -0.8) - P(z < -3) = 0.2119 - 0.0013 = 0.2106.