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1. Problem 1 is adapted from Problem 29 at the end of Chapter 11. Please use Excel to solve this problem and submit your Excel file. The problem is as follows:

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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.

1. 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.)

2. What is the probability that the demand will be between 5000 and 7000 yards?

3. 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%.)

1. Problem 2 is adapted from the Problem 39 at the end of Chapter 11. Please solve this problem in Excel and submit your Excel spreadsheet. The problem is as follows:

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

Assume that SOL test scores are normally distributed.

1. Compute the mean and standard deviation for these data.

2. Determine the probability that a student at the high school will pass the test.

3. How many percent of students will receive a score between 75 and 95?

4. What score will put a student in the bottom 15% in SOL score among all students who take the test?

5. What score will put a student in the top 2% in SOL score among all students who take the test?

1. The average male drinks 2 L of water when active outdoors (with a standard deviation of 0.8L). You are planning a full day nature trip for 100 men and will bring 210 L of water. What is the probability that you will run out? Please solve this problem in Excel and submit your Excel file.

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