1. According to the United National Environmental Program and World Health Organization, in Mumbai, India, air pollution standards for particulate matter are exceeded an average of 5.6 days in every three-week period. Assume that the distribution of number of days exceeding the standards per three-week period is Poisson distributed.

(Round your answers to 4 decimal places.)

a.What is the probability that the standard is not exceeded on any day during a three-week period?

b.What is the probability that the standard is exceeded exactly six days of a three-week period?

c.What is the probability that the standard is exceeded 15 or more days during a three-week period?

2. Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1.2 collisions every four months.

(Round your answers to 4 decimal places.)

a.What is the probability of having no collisions occur over a four-month period?

b.What is the probability of having exactly two collisions in a two-month period?

c.What is the probability of having one or fewer collisions in a six-month period?

3.A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distributed. a.What is the probability of selecting a carton and findingone defective pen? b.What is the probability of findingsevenor more defective pens in a carton? c.Suppose a purchaser of these pens will quit buying from the company if a carton contains more thanfivedefective pens. What is the probability that a carton contains more thanfivedefective pens?

(Round your answers to 4 decimal places when calculating) a.P(x=1| = 1.2) = b.P(x7| = 1.2) = c.P(x>5| = 1.2) =