Harper\'s Index reported that the number of (Orange County, California) convicte

Question

Harper's Index reported that the number of (Orange County, California) convicted drunk drivers whose sentence included a tour of the morgue was 518, of which only 1 became a repeat offender. (a) Suppose that of 1011 newly convicted drunk drivers, all were required to take a tour of the morgue. Let us assume that the probability of a repeat offender is still p = 1/518. Explain why the Poisson approximation to the binomial would be a good choice for r = number of repeat offenders out of 1011 convicted drunk drivers who toured the morgue.

What is to the nearest tenth?


(b) What is the probability that r = 0? (Use 4 decimal places.)

(c) What is the probability that r > 1? (Use 4 decimal places.)

(d) What is the probability that r > 2? (Use 4 decimal places.)


(e) What is the probability that r > 3? (Use 4 decimal places.

please help solve, TI-84

Explanation / Answer

Here N = 1011 and p = 1/518

For Binomial Distribution with large n, calculating the mass function is pretty complex. So for those complex “large” Binomials (n 100) and for small p (usually 0.01), we can use a Poisson with = n (20) to approximate it!

What is to the nearest tenth?

= 1011 * ( 1/518) = 1.95 = 2.0

(b) What is the probability that r = 0?

P( r = 0; 2.0) = (2.0)0 e-2/ 0! = 0.1353

(c) What is the probability that r > 1?

P( r > 1; 2.0) = = 1 - P( r = 0; 2.0) - P( r = 1; 2.0) = 1 - (2.0)1 e- 2.0/ 1! - (2.0)0 e-2.0/ 0!

= 1 - 0.2707 - 0.1353 = 0.5940

(d) What is the probability that r > 2?

P( r > 2; 2.0) = = 1 - P( r = 0; 2.0) - P( r = 1; 2.0) - P( r = 2; 2.0)

= 1 - (2.0)1 e- 2.0/ 1! - (2.0)0 e-2.0/ 0! -  (2.0)2 e-2.0/ 2!

= 1 - 0.2707 - 0.1353 - 0.2707 = 0.3233

(e) What is the probability that r > 3?

P( r > 3 ; 2) = = 1 - P( r = 0; 2) - P( r = 1; 2) - P( r = 2; 2) - P( r = 3; 2)

= 1 - (2)1 e- 2/ 1! - (2)0 e-2/ 0! -  (2)2 e-2/ 2! -  (2)3 e-2/ 3!

= 1 - 0.2707 - 0.1353 - 0.2705 - 0.1804 = 0.1429

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