# Z-scores and Normal Distributions Review

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NAME: 3.2 HW

Be sure to write probability notation!

1. A packing machine is set to fill a cardboard box with a mean of 16.1 ounces of cereal. Suppose the amounts per box form a normal distribution with a standard deviation equal to 0.04 ounce.

a. What percentage of the boxes will end up with at least 16.1 oz. of cereal?

b. What is the probability that a box has less than 16.04 oz.?

c. What is the probability that a box contains more than 16.18 oz?

d. What percentage of boxes contain between 16.03 and 16.15 oz.?

e. 72% percent of the boxes will contain more than what number of ounces?

f. What number of ounces corresponds to the 15th percentile?

g. The middle 80% of the boxes will be between what two weights?

2. A water fountain is designed to dispense a volume of 12.2 oz. with a std. deviation of 0.5 oz.

a. What percentage of cups ends up with at least 12 oz.?

b. What proportion of cups have between 11.9 and 12.7 oz of water?

c. 65% of the cups contain more than how much water?

d. Find the 90th percentile for the amount of water dispensed.

e. Find the IQR of the water fountain

NAME: 3.2 HW

Be sure to write probability notation!

1. A packing machine is set to fill a cardboard box with a mean of 16.1 ounces of cereal. Suppose the amounts per box form a normal distribution with a standard deviation equal to 0.04 ounce.

a. What percentage of the boxes will end up with at least 16.1 oz. of cereal?

b. What is the probability that a box has less than 16.04 oz.?

c. What is the probability that a box contains more than 16.18 oz?

d. What percentage of boxes contain between 16.03 and 16.15 oz.?

e. 72% percent of the boxes will contain more than what number of ounces?

f. What number of ounces corresponds to the 15th percentile?

g. The middle 80% of the boxes will be between what two weights?

3. A water fountain is designed to dispense a volume of 12.2 oz. with a std. deviation of 0.5 oz.

a. What percentage of cups ends up with at least 12 oz.?

b. What proportion of cups have between 11.9 and 12.7 oz of water?

c. 65% of the cups contain more than how much water?

d. Find the 90th percentile for the amount of water dispensed.

e. Find the IQR of the water fountain

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