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

m1=1.4 ounces

s1 = 0.3 ounce

m2 = 2.5 ounces

s2 = 0.4 ounce

Now, m1 - m2 follows a normal distribution

So, mean of difference =X= 1.4 - 2.5 = -1.1 ounce

std dev = sqrt(s1^2 + s2^2) , as the amouns poured in both bowls is independent

= sqrt(0.3^2 + 0.4^2) = 0.5 ounce

We want P(X>0) = P(Z>(0-(-1.1))/0.5) = P(Z > 2.2) = 0.014

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.