Question

Recent crime reports indicate that 16.3 motor vehicle thefts occur every hour in Canada. Assume that the distribution of thefts per hour can be approximated by a Poisson probability distribution. a. Calculate the probability exactly four thefts occur in an hour.(Round the final answer to 5 decimal places.) Probability b. What is the probability there are no thefts in an hour? (Round the final answer to 5 decimal places.) Probability c. What is the probability there are at least 20 thefts in an hour? Use excel or online calculator to find the answer. (Round the final answer to 5 decimal places.) Probability

statistics

Answer 1

Let ,

Therefore , the probabiliy mass function of X is ,

; x=0,1,2,........,

=0 ; otherwise

By using excel ,

X	X!	16.3^X	P(X=x)
0	1	1	8.33681E-08
1	1	16.3	1.3589E-06
2	2	265.69	1.1075E-05
3	6	4330.747	6.01744E-05
4	24	70591.18	0.000245211
5	120	1150636	0.000799386
6	720	18755370	0.002171666
7	5040	3.06E+08	0.00505688
8	40320	4.98E+09	0.010303393
9	362880	8.12E+10	0.018660589
10	3628800	1.32E+12	0.03041676
11	39916800	2.16E+13	0.045072109
12	479001600	3.52E+14	0.061222947
13	6227020800	5.73E+15	0.076764157
14	87178291200	9.35E+16	0.089375412
15	1.30767E+12	1.52E+18	0.097121281
16	2.09228E+13	2.48E+19	0.098942305
17	3.55687E+14	4.05E+20	0.09486821
18	6.40237E+15	6.6E+21	0.085908434
19	1.21645E+17	1.08E+23	0.073700394
20	2.4329E+18	1.75E+24	0.060065821

a) P(X=4) = 0.00025

Therefore , the probability there are excatly four thefts in an hour is 0.00025

b) P(X=0) = 0.00000

Therefore , the probability there are no thefts in an hour is 0.00000

c)

Therefore , the probability there are at least 20 thefts in an hour is 0.20930.