Question

The time it takes to bake a Betty Crocker Supermoist Fudge Cake is normally distributed with a mean of 45 minutes and a variance of 26 minutes^2. Let baking time, in minutes, be represented by random variable X. P(x1 < X < 49) = 0.0910. Find x1 (in minutes).

Answer 1

= 45, = sqrt(26)

We convert this to standard normal as

P( X < x) = P( Z < x - / )

Therefore,

P(x1 < X < 49) = 0.0910

P( X < 49) - P( X < x1) = 0.0910

P( Z < 49 - 45 / sqrt(26) ) - P( X < x1) = 0.0910

P( Z < 0.7845) - P( X < x1) = 0.0910

0.7836 - P( X < x1) = 0.0910

P( X < x1) = 0.6926

P( Z < x1 - 45 / sqrt(26) ) = 0.6926

From Z table, z-score for the probability of 0.6926 is 0.5033

Therefore,

x1 - 45 / sqrt(26) = 0.5033

Solve for x1,

x1 = 47.566 minutes