Consider a Poisson random variable with ? = 3. Use the Poisson formula to calculate the following probabilities:
a. P(x = 0)
b. P(x = 1)
c. P(x > 1)
2. (Page 193, # 5.43) Airport Safety The increased number of small commuter planes in major airports has heightened concern over air safety. An eastern airport has recorded a monthly average of five near misses on landings and takeoffs in the past 5 years.
- Find the probability that during a given month there are no near misses on landings and
- takeoffs at the airport.
- Find the probability that during a given month there are five near misses.
- Find the probability that there are at least five near misses during a particular month.
3. (Page 194, # 5.45, # 5.46) Accident Prone According to a study conducted by the depart- ment of Pediatrics at the University of California, San Francisco, children who are injured two or more times tend to sustain these injuries during a relatively limited time, usually 1 year or less. Assume the average number of injuries per year for school-age children is two.
- Find the probability of a school-age child sustains two injuries during the year.
- Find the probability of a school-age child sustains two or more injuries during the year.
- Find the probability of a school-age child sustains at most one injuries during the year.
- Calculate the mean and standard deviation for x, the number of injuries per year sustained by a school-age child.
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