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# Mean, variance, confidence interval

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1. Compute the mean and variance of the following discrete probability distribution.
x P(x )
0 .20
1 .40
2 .30
3 .10

2. In a binomial situation n = 4 and &#960; = .25. Determine the probabilities of the following events using the binomial formula.
a. x = 2 b. x = 3

3. A cola-dispensing machine is set to dispense on average 7.00 ounces of cola per cup. The standard deviation is 0.10 ounces. The distribution of amounts dispensed follows a normal distribution.
a. What is the probability that the machine will dispense between 7.10 and 7.25 ounces of cola?
b. What is the probability that the machine will dispense 7.25 ounces of cola or more?
c. What is the probability that the machine will dispense between 6.80 and 7.25 ounces of cola?

4. The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 90 percent confidence interval, what is the value of t?
d. Develop the 90 percent confidence interval for the population mean.

5. The Confabulator Construction Company limits its business to constructing decks. The mean time to construct one of their standard decks is 8 hours for a two-person construction crew. The information is based on a sample of 40 decks recently constructed. The standard deviation of the sample was 3 hours.
a. Determine a 90 percent confidence interval for the population mean.
b. Would it be reasonable to conclude that the population mean is actually 9 hours? Justify your answer.