Chapter 6, Problem 3UTA

Although tables of binomial probabilities can be found in most libraries, such tables are often inadequate. Either the value of p(the probability of success on a trial) you are looking for is not in the table, or the value of n (the number of trials) you are looking for is too large for the table. In Chapter 7, we will study the normal approximation to the binomial. This approximation is a great help in many practical applications. Even so. we sometimes use the formula for the binomial probability distribution on a computer or graphing calculator to compute the probability we want.

Applications

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.

Location	Long-Term Mean % of Clear Days in Dec
Juneau, Alaska	18%
Seattle. Washington	24%
Hilo. Hawaii	36%
Honolulu, Hawaii	60%
Las Vegas, Nevada	75%
Phoenix, Arizona	77%

Adapted from Local Climatological Data, U.S. Weather Bureau publication, “Normals. Means, and Extremes” Table.

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.

Estimate the probability that Juneau will have at most 7 clear days in December.