Problem 1: Consider the following data:
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x
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1
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2
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3
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4
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5
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P(X = x)
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0.1
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0.3
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0.2
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0.2
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0.2
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Step 1: Find the expected value E(X).
Step 2: Find the standard deviation.
Problem 2: Trucks in a delivery fleet travel a mean of 110 miles per day with a standard deviation of 31 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 82 and 159 miles in a day.
Problem 3: Consider the table below, which describes the rate of economic growth (Xi) and the rate on the S&P 500 (yi). Calculate the covariance and the correlation coefficient for the data set.
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Economic Growth % (xi)
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S&P 500 Returns % (yi)
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2.1
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8
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2.5
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12
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4.0
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14
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3.6
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10
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