Question

A study of a disease reveals that there is an average of 1 case every 22 square miles. Residents of a town that has an area of 10 square miles are concerned because there are two cases in their area. The state’s Department of Health has decided to investigate further if the probability of getting two or more cases in this town is less than 0.05. Does the Department of Health investigate further?

Answer 1

Answer:

Given that,

A study of a disease reveals that there is an average of 1 case every 22 square miles. Residents of a town that has an area of 10 square miles are concerned because there are two cases in their area.

The state’s Department of Health has decided to investigate further if the probability of getting two or more cases in this town is less than 0.05.

Does the Department of Health investigate further?:

Average case=1 every 22 square miles

=1/22 every square miles

=(1/22) 10 every 10 square mile

=0.4545 every 10 square mile

Let X be the number of cases in the town

X Poisson (0.4545)

P(Two or more cases):

P(X 2)=1-P(X < 2)

=1-0.92327 (Since, from Z-score table)

=0.07673

As the probability is not less than 0.05, So department should not investigate further.