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# Probability questions on Binomial and normal distribution

1. Assume a restaurant business succeeds 60% of the time. Suppose that there are three such restaurants open in your city. When they don?t compete with one another, it is reasonable to believe that their relative success would be independent. [Hint: use binomial probability distribution function in Megastat or Phstat]

A) What is the probability that all the three businesses succeed?

B) What is the probability that all the three businesses fail?

C) What is the probability that at least one business succeeds?

2. A recent study of the hourly wages of maintenance crews for major airlines showed that the mean hourly salary was \$16.50, with a standard deviation of \$3.50. If we select a crew member at random, what is the probability the crew member earns: [use Phstat, probability & probability distribution, normal function].

Exactly \$18.00 per hour?
Between \$16.50 and \$20.00 per hour?
More than \$20.00 per hour?
Less than \$15.00 per hour?
3. Explain whether the width of a confidence interval would increase, decrease, or remain the same as a result of each of the following changes:

a) The sample size is doubled, from 400 to 800 ____________

b) The population size is doubled, from 25 million to 50 million ____________

c) The level of confidence is lowered from 95% to 90% ____________

#### Solution Summary

The solution gives step by step procedure for the calculation of probability of normal and binomial variables.

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