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 1.4 ounces and a standard deviation of 0.30 ounce. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.40 ounce. A student opens a new box of cereal and pours one large and one small bowl. Assume that the amounts poured into the two bowls are independent. If the difference follows a Normal model, what is the probability the small bowl contains more cereal than the large one? Round to 3 decimal places as needed.

Explanation / Answer

Result:

The amount of cereal that can be poured into a small bowl varies with a mean of 1.4 ounces and a standard deviation of 0.30 ounce. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.40 ounce. A student opens a new box of cereal and pours one large and one small bowl. Assume that the amounts poured into the two bowls are independent. If the difference follows a Normal model, what is the probability the small bowl contains more cereal than the large one? Round to 3 decimal places as needed.

L: amount in large bowl

S: amount in small bowl.

E( S-L) = E(S) –E(L) = 1.4-2.5 = -1.1

Var( S-L) = Var(S)+Var(L) =0.30^2+0.40^2 =0.25

SD( S-L) = sqrt(0.25) =0.5

S_L follows N( -1.1, 0.5)

Z value for 0, z=(0-(-1.1))/0.5 =2.2

P( Z > 2.2) =0.0139

Answer: 0.014   ( 3 decimals)

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