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 1.6 ounces and a standard deviation of 0.3 ounce. A large bowl holds a mean of 2.7 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. ounce(s) (Type an integer or a decimal.) b) What is the standard deviation? ounce(s) (Round to two decimal places as needed.) 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? Round to three decimal places as needed.)

Explanation / Answer

a) expected ampunt of cereal left in box E(D)=E(A)-E(B+C) =16.2-1.6-2.7=11.9

b) std deviation =(0.32+0.42+0.12)1/2 =0.5099

c)probability =P(X>13) =1-P(X<13) =1-P(Z<(13-11.9)/0.5099)=1-P(Z<2.1573)=1-0.9845=0.015

plpease revert for any clarificaiton required

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