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Probability

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Please provide explanation and answers to these questions.

1. The Speed master IV automobile gets an average 22.0 miles per gallon in the city. The standard deviation is 3 miles per gallon. Assume the variable is normally distributed. Find the probability that on any given day, the car will get more than 26 miles per gallon when driven in the city. Put answer in decimal form.

2. For a specific year, Americans spent an average of $71.12 for books. Assume the variable is normally distributed. If the standard deviation of the amount spent on books is $8.42, find these probabilities for a randomly selected American. Put answer in percent form.
a. He or she spent more than $60 per year on books.

3. The average time a visitor spends at the Renzie Park Art Exhibit is 62 minutes. The standard deviation is 12 minutes. If a visitor is selected at random, find the probability that he or she will spend the following amount of time at the exhibit. Assume the variable is normally distributed. Please put in percent form.
a. At least 82 minutes.

4. The average time a visitor spends at the Renzie Park Art Exhibit is 62 minutes. The standard deviation is 12 minutes. If a visitor is selected at random, find the probability that he or she will spend the following amount of time at the exhibit. Assume the variable is normally distributed. Please put in percent form.
b. At most 50 minutes.

5. The average time a person spends at Barefoot Landing Seaquarium is 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributed. If a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium. Please put answer in decimal form.
a. At least 120 minutes.

6. The average time a person spends at Barefoot Landing Seaquarium is 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributed. If a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium. Please put answer in decimal form.
b. At most 80 minutes.

7. In order to qualify for letter sorting, applicants are given a speed-reading test. The scores are normally distributed with a mean of 80 and a standard deviation of 8. If only the top 15% of the applicants are selected, find the cutoff score. Round to two decimal places.

8. For an educational study, a volunteer must place in the middle 50% on a test. If the mean for the population is 100 and the standard deviation is 15, find the two limits (upper and lower) for the scores that would enable a volunteer to participate in the study. Assume the variable is normally distributed. Round to two decimal places.

9. For a certain group of individuals, the mean hemoglobin level in the blood is 21.0 grams per milliliter (g/ml). The standard deviation is 2 g/ml. If a sample of 25 individuals is selected, find the probability that the mean will be greater than 21.3 g/ml. Assume the variable is normally distributed. Please put you answer in decimal form.

10. The average age of chemical engineers is 37 years with a standard deviation of 4 years. If an engineering firm employs 25 chemical engineers, find the probability that the average age of the group is greater than 38.2 years old. Please put you answer in decimal form.

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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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