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Probabilities

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A. Scores of high school students on a national mathematics exam in Egypt were normally distributed with a mean of 86 and a standard deviation of 4.

1. What is the probability that a randomly selected student will have a score of 80 or higher?
2. If there were 97,680 students with scores higher than 91, how many students took the test?

B. In a study of television viewing habits among married couples, a researcher found that for a popular Saturday night program, 25% of the husbands viewed the program regularly and 30% of the wives viewed the program regularly. The study found that, for couples where the husband watches the program regularly, 80% of the wives also watch regularly. What is the probability that both the husband and the wife watch the program regularly?

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Solution Summary

What is the probability that both the husband and the wife watch the program regularly?

$2.19
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The probability

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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