Find Probability

Question

Assume the random variable x is normally distributed with mean μ=84 and standard deviation σ=5.



Find the indicated probability.

​P(67<x<79​)

Answer 1

For mean 84 and SD = 5, z = (x - 84)/5

Transform P(67 < x < 79) to P( (67-84)/5 < z < (79 - 84)/5) = P(-3.4 < z < -1) = P(z < -1) - P(z < -3.4) = 0.1587 - 0.0003 = 0.1584.