Question

Rabies is an often-fatal disease typically transmitted through the bite of an infected animal. The state of Florida has been recording all known cases of rabies for the past 20 years, with data indicating an average rate of 3.6. cases of rabies per week. Let X be the count of rabies cases reported in a given week.
a) The mean of X = __Answer 1__. Round your answer to one decimal place.

b) The standard deviation of X = __Answer 2__. Round your answer to 3 decimal places.

c) The probability that there would be no case of rabies reported in a given week is __Answer 1__. Round your answer to 4 decimal places.

d) The probability that there would be at least 1 case reported in a given week is __Answer 2__. Round your answer to 4 decimal places.

Answer 1

Answer:

a) 3.6

b) 1.897

c)0.0273

d) 0.9727

Step-by-step explanation:

Rabies has a rare occurrence and we can assume that events are independent. So, X the count of rabies cases reported in a given week is a Poisson random variable with μ=3.6.

a)

The mean of a Poisson random variable X is μ.

mean=E(X)=μ=3.6.

b)

The  standard deviation of a Poisson random variable X is √μ.

standard deviation=S.D(X)=√μ=√3.6=1.897.

c)

The probability for Poisson random variable X can be calculated as

P(X=x)=(e^-μ)(μ^x)/x!

where x=0,1,2,3,...

So,

P(no case of rabies)=P(X=0)=e^-3.6(3.6^0)/0!

P(no case of rabies)=P(X=0)=0.0273.

d)

P(at least one case of rabies)=P(X≥1)=1-P(X<1)=1-P(X=0)

P(at least one case of rabies)=1-0.0273=0.9727