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# Probability and Probability Distributions

1) In a certain town, 60% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults)who have a college degree. Find the variance for the probability distribution.
x P(x)
0 0.0256
1 0.1536
2 0.3456
3 0.3456
4 0.1296

2) An airline estimates that 98% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?

Use the Poisson Distribution to find the indicated probability.
3) A mountain search and rescue team receives an average of &#956; = 0.75 calls per day. Find the probability that on a randomly selected day, they will receive fewer than two calls.

#### Solution Preview

(1) Mean = Sum of [x * P(x)] = 0 + 1(0.1536) + 2(0.3456) + 3(0.3456) + 4(0.1296)] = 2.4

Deviations of x from the mean value are: -2.4, -1.4, -0.4, 0.6, 1.6

Sum of the ...

#### Solution Summary

Step-by-step answers worked out for the questions.

\$2.19