The amount of cereal that can be poured into a small bowl varies with a mean of

Question

The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.8 ounces with a standard deviation of 0.3 ounces. You open a new box of cereal and pour one large bowl and one small bowl. Complete parts (a) through (f) below, (c) If the difference follows the normal model, what's the probability that the small bowl contains more cereal than the large one? (b) What are the mean and standard deviation of the total amount of cereal in the two bowls? (e) If the total follows a normal model, what's the probability you poured out more than 4.7 ounces of cereal in the bowls together?

Explanation / Answer

c)here let small bowl is A and large bowl is B

here mean of B-A =2.8-1.5 =1.3

and std deviation of B-A =(0.32+0.32)1/2 =0.4243

hence P(B-A<0) =P(Z<(0-1.3)/0.4243)= P(Z<-3.0641)=0.0011

d) mean of A+B=2.8+1.5=4.3

and std deviation of A+B =0.4243

e) P(A+B>4.7)=1-P(A+B<4.7)=1-P(Z<(4.7-4.3)/0.4243)=1-P(Z<0.9428)=1-0.8271=0.1729

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