Question

the time it takes to bake a Betty crocker supermoist fudge cake is normally distributed with a mean of 39 minutes and a variance of 28 minutes^2. let baking time, in minutes, be represented by random variable x.

1) p(x1<X<43)=0.1270. Find x1

Answer 1

Solution :

Solution :

Given that ,

mean = = 39

variance = 28

standard deviation = = 5.2915

P(X1 < X < 43) = 0.1270

P((X1 - 39)/ 5.2915) < (x - ) /  < (43 - 39) / 5.2915) = 0.1270

P(X1 < Z < 0.756) = 0.1270

P(Z < 0.756) - P((X1 - 39)/ 5.2915) = 0.1270

0.7752 - P((X1 - 39)/ 5.2915) = 0.1270

P((X1 - 39)/ 5.2915) = 0.7752 - 0.1270 = 0.6482

P(z < 0.38) = 0.6482

z = 0.38

X1 = 0.38 * 5.2915 + 39 = 41

P(41 < X < 43) = 0.1270