Question

The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally distributed with a mean of 38 minutes and a variance of 35 minutes ^2. Let baking time, in minutes, be represented by random variable X. P(x1<X<42)= 0.1090. Find X1. IMPORTANT: Make sure you carry all decimals until you reach your answer, then round to four decimals.

Answer 1

P(x1 < X < 42) = 0.1090

or, P((x1 - )/ < (X - )/ < (42 - )/) = 0.1090

or, P((x1 - 38)/ < Z < (42 - 38)/) = 0.1090

or, P((x1 - 38)/ < Z < 0.68) = 0.1090

or, P(Z < 0.68) - P(Z < (x1 - 38)/) = 0.1090

or, 0.7517 - P(Z < (x1 - 38)/) = 0.1090

or, P(Z < (x1 - 38)/) = 0.6427

or, (x1 - 38)/ = 0.36

or, x1 = 0.36 * + 38

or, x1 = 40.1298