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A warehouse distributor of carpet faces a normally distributed demand for its carpet.
1. A warehouse distributor of carpet faces a normally distributed demand for its carpet. The average demand for carpet from the stores that purchase from the distributor is 4,500 yards per month, with a standard deviation of 900 yards.
a. Suppose the distributor keeps 6,000 yards of carpet in stock during a month. What is the probability that a customer’s order will not be met during a month? (This situation is referred to as a stockout.)
b. What is the probability that the demand will be between 5000 and 7000 yards?
c. How many yards of carpet should this warehouse distributor order from its supplier to ensure that 97% of the demand is met? (The percent of customer demand/orders satisfied is referred to as service level. In this question, the service level is 97%.)
2. The state of Virginia has implemented a Standard of Learning (SOL) test that all public school students must pass before they can graduate from high school. A passing grade is 75. Montgomery County High School administrators want to gauge how well their students might do on the SOL test, but they don’t want to take the time to test the whole student population. Instead, they selected 20 students at random and gave them the test. The results are as follows:
83 79 56 93
48 92 37 45
72 71 92 71
66 83 81 80
58 95 67 78
