Question

The Honolulu advertiser stated that in Honolulu there was an average of 661 burglaries per 400,000 households in a given year. In the Kohola drive neighborhood there are 317 homes. Let r be the number of homes that will be burglarized in a year. Compute the probability for r > or equal to 2 round your answer to the nearest ten thousandth.

A)0.3010
B) 0.1013
C) 0.0144
D) 0.0902
E) 0.0369

Answer 1

Answer:

D) 0.0902

Step-by-step explanation:

Data provided in the question:

Probability of burglary, p = $\frac{661}{400,000}$

= 0.00165      

q = 1 - p                

or                    

q = 1 - 0.00165                      

or                    

q = 0.99835                              

Now,

P(r ≥ 2) = 1 - P(r < 2)

= 1 - [ P(0) + P(1) ]

= 1 - [  $^{317}C_0(0.00165)^0(0.99835)^{317-0}+^{317}C_1(0.00165)^1(0.99835)^{317-1}$ ]

[ as P(x) = $^nC_rp^rq^{n-r}$]

= 1 - [ 0.593 + 0.3168]

= 1 - 0.9098

= 0.0902

Hence,

Option (D) 0.0902