Solve the following problems:
Situation: Fifteen (15) companies all bid on oil leases. The following data is a small part of the records on past bids. All monetary amounts are in millions of dollars.
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Leases
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Signals
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Proven Value
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Company 1
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Company 2
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$105.5
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$99.5
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$107.4
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$107.5
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$97.1
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$101.5
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$98.7
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$101.5
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$103.7
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Q1. Compute the mean error in the signals.
Q2. Let R be the continuous random variable giving the error in a geologist's estimate for the value of a lease. Experience allows us to assume that R is normal, with mR = 0 and sR = 10 million dollars. Suppose that the 15 companies form 3 bidding rings of equal sizes. Let M be the random variable giving the mean of the errors for a set of signals for the companies in one of the bidding rings. Compute the standard deviation, σM, for M? Round your answer to 3 decimal places.
A normal random variable X gives the number of ounces of soda in a randomly selected can from a given canning plant. It is known that the mean of X is close to 8 ounces and that σX = 0.2 ounces. Let x‾ be the mean of a random sample of size n = 4 soda cans.
Q3. Compute σx . Sketch a graph of the probability density function for x‾. Use standard deviations to explain why the mean of a sample of size n = 16 cans would be likely to give a better estimate for μX than would the mean of a sample of size n = 4 cans.