Statistics: The CLT

Question

Suppose x has a distribution with 𝜇 = 78 and 𝜎 = 8.

Find P(74 ≤ x ≤ 79). (Round your answer to four decimal places.)

Answer 1

translate limits of inequality to standard normal variable (z) = (x - mean)/SD = (x = 78)/8

so P(74 <= x <= 78) = P( (74-78)/8 < z < (78-78)/8) = P(-0.5 < z < 0) = P(z < 0) - P(z < -0.5) = 0.5 - 0.3085 = 0.1915