Question

The amount of cereal that can be poured into a small bowl varies with a mean of 1.7

ounces and a standard deviation of

0.3 ounce. A large bowl holds a mean of

2.8 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. Assume that the amounts poured into the two bowls are independent. Complete parts​ (a) through​ (f) below.

​a) How much more cereal does the student expect to be in the large​ bowl?

​b) What is the standard deviation of this​ difference?

​c) If the difference follows a Normal​ model, what is the probability the small bowl contains more cereal than the large​ one?

d) What are the mean and standard deviation of the total amount of cereal in the two​ bowls? The standard deviation is?

​e) If the total follows a Normal​ model, what is the probability the student poured out more than 5.2 ounces of cereal in the two bowls​ together?

f) The amount of cereal the manufacturer puts in the boxes is a random variable with a mean of

16.3 ounces and a standard deviation of 0.2 ounce. Find the expected amount of cereal left in the box and the standard deviation.

The expected amount of cereal left in the box is ounce(s).

The standard deviation is ​ounce(s).

Answer 1