The following percentages were obtained over many years of observation by the U.S. Weather Bureau. All data listed are for the month of December.
In the locations listed, the month of December is a relatively stable month with respect to weather. Since weather patterns from one day to the next are more or less the same, it is reasonable to use a binomial probability model.
1. Let r be the number of clear days in December. Since December has 31 days, 0 ≤ r ≤ 31. Using appropriate computer software or calculators available to you, find the probability P(r) for each of the listed locations when .
2. For each location, what is the expected value of the probability distribution? What is the standard deviation? You may find that using cumulative probabilities and appropriate subtraction of probabilities, rather than addition of probabilities, will make finding the solutions to Applications 3 to 7 easier.
3. Estimate the probability that Juneau will have at most 7 clear days in December.
4. Estimate the probability that Seattle will have from 5 to 10 (including 5 and 10) clear days in December.
5. Estimate the probability that Hilo will have at least 12 clear days in December.
6. Estimate the probability that Phoenix will have 20 or more clear days in December.
7. Estimate the probability that Las Vegas will have from 20 to 25 (including 20 and 25) clear days in December.
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