Question 1
The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes?
◦ at least 75%
◦ at least 0%
◦ at least 89%
◦ at least 95%
Question 2
By law, a box of cereal labeled as containing 18 ounces must contain at least 18 ounces of cereal. The machine filling the boxes produces a distribution of fill weights with a mean equal to the setting on the machine and with a standard deviation equal to 0.03 ounce. To ensure that most of the boxes contain at least 18 ounces, the machine is set so that the mean fill per box is 18.09 ounces. Assuming nothing is known about the shape of the distribution, what can be said about the proportion of cereal boxes that contain less than 18 ounces.
◦ The proportion is at least 89%.
◦ The proportion is at most 5.5%.
◦ The proportion is less than 2.5%.
◦ The proportion is at most 11%.
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