Question

The amount of cereal that can be poured into a small bowl varies with a mean of 1.3 ounces and a standard deviation of 0.3 ounce. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounce. A student opens a new box of cereal and pours one large and one small bowl. Suppose that the amount of cereal the manufacturer puts in the boxes is a random variable with a mean of 16.2 ounces and a standard deviation of 0.1 ounce. Complete parts​ (a) through​ (c) below.

​a) Find the expected amount of cereal left in the box.

​b) What is the standard​ deviation?

​c) If the weight of the remaining cereal can be described by a Normal​ model, what's the probability that the box still contains more than 13 ounces?

Answer 1

let initial amount is A , while that in small and large bowl is B and C

a)expected amount left E(D)=E(A-B-C) =16.2-1.3-2.5 =12.4

b)  standard​ deviation =sqrt(0.3²+0.4²+0.1²) =0.5099

c)

P(D>13) =P(Z>(13-12.4)/0.5099)=P(Z>1.18)=0.1190