Question

The number of houses sold by an estate agent follows a Poisson distribution, with a mean of 2 per week.

a.Find the probability that in the next 4 weeks the estate agent sells, 1 exactly 3 houses, 2 more than 5 houses.

The estate agent monitors sales in periods of 4 weeks.

b.Find the probability that in the next twelve of these 4 week periods there are exactly nine periods in which more than 5 houses are sold.

The estate agent will receive a bonus if he sells more than 25 houses in the next 10 weeks.

c.Use a suitable approximation to estimate the probability that the estate agent receives a bonus.

Answer #1

Let X be the number of houses that an agent sold in a
day. Suppose X has the following probability mass function
(pmf):
y
0
1
2
3
p(y)
0.5
0.33
0.14
0.03
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