Question

Please show all work and give a detailed explanation.

According to ghost hunters, large cities have, on average, 9 haunted houses each. As far as we know, it is unpredictable which houses will be haunted; and just because one house is haunted, that does not mean any of its neighbors will or will not be haunted. a) What is the standard deviation of the number of haunted houses in a large city? b) What is the probability that 5 or fewer haunted houses will be found in a city?

Answer 1

here this is poisson distribution with parameter λ =9

a)

standard deviation σ=√λ=

3.000

b)

P(X<=5) =P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

=e^-99⁰/0!+ e^-99¹/1!+e^-99²/2!+e^-99³/3!+e^-99⁴/4!+e^-99⁵/5! =0.1157