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Probability

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The Oil Price Information Center reports the mean price per gallon of regular gasoline is 3.26 with a population standard deviation of 0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed.

a.) What is the standard error of the mean in this experiment?
b.) What is the probability that the sample mean is between $2.98 and $3.02?
c.) What is the probability that the difference between the sample mean and the population mean is less than 0.01?
d.) What is the likelihood the sample mean is greater than $3.08?

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A young engineer has invented holographic mobile phones and has approached a venture capital company to invest in it. The venture capital company considers the product to be an all or nothing product: either everyone will want one because everyone else has one or no one will want one because there will be no one to use it with. The company believes that the probability that it will take off netting them a profit of $2000000 is 0.14. If it doesn't take off then they expect that they would loose $200000. They are considering using a consumer survey to gather more information. However, the company has experience that shows that the probability that the consumer survey will predict success for a product that will fail is 0.24, and the probability that the consumer survey will predict failure when the product will be a success is 0.07. What is the monetary value of the information from a consumer survey to the venture capital company in this case? (ie what is the maximum that they should spend on a consumer survey)?

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