The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounce. A large bowl holds a mean of 2.4 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? --------- ounce(s) (Type an integer or a decimal.)
b) What is the standard deviation of this difference? -------ounce(s) (Round to two decimal places as needed.)
c) If the difference follows a Normal model, what is the probability the small bowl contains more cereal than the largeone? ------- (Round to three decimal places as needed.)
d) What are the mean and standard deviation of the total amount of cereal in the two bowls? The mean is --------ounce(s). (Type an integer or a decimal.)
The standard deviation is ---------ounce(s). (Round to two decimal places as needed.)
e) If the total follows a Normal model, what is the probability the student poured out more than 4.6 ounces of cereal in the two bowls together? ------- (Round to three decimal places as needed.)
f) The amount of cereal the manufacturer puts in the boxes is a random variable with a mean of 16.5 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). (Type an integer or a decimal.)
The standard deviation is -------- ounce(s). (Round to two decimal places as needed.)
