The time it takes to bake a Betty Crocker Supermoist Fudge C

The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally distributed with a mean of 44 minutes and a variance of 42 minutes^2. Let baking time, in minutes, be represented by random variable

Solution

P(x1 < x < 47) = P(X<47) - P(X<x1) = 0.1020

or, P(Z< (47-44) / root(42) ) - P(Z < (x1-44) / root(42)) = 0.1020

or, 0.6783 - P(Z < (x1-44) / root(42)) = 0.1020

or, P(Z < (x1-44) / root(42)) = 0.6783 - 0.1020 = 0.5763

We know,

P(Z < 0.192) = 0.5763

So (x1-44) / root(42) = 0.192

x1 = [0.192 * root (42)] + 44 = 45.2443