3. Alternative Game of Thrones facts have been discovered in the archives! Jon S

Question

3. Alternative Game of Thrones facts have been discovered in the archives! Jon Snow's campaign to Make The Wall Great Again involves teaching 1000 wildlings how to wield a dragonglass (obsidian) sword. (a) Jon wants to have at least 3 wildling guards who know how to wield a dragonglass sword. If each wildling can independently master the sword with probability 0.002, find the prob- (b) Approximate the probability you found in part (a) with a Poisson distribution. Do not (c) Is using a Poisson distribution for an approximation a good choice in this case? Explain ability that Jon will have his guards. leave your answer in an infinite sum. your answer in a few brief sentences.

Explanation / Answer

Question 3

Number of wildlings = 1000

Probability of making them master in sword wielding = 0.002

(a) By binomial distribution :

n = 1000 ; p = 0.002

If X is the number of wildlings mastered in dragonglass sword.

Pr(X >=3 ; 1000; 0.002) = 1 - [ P(0) + P(1) + P(2) ]

= 1 - [1000C0 (0.002)0(0.998)1000 + 1000C1 (0.002)1(0.998)999 + 1000C2 (0.002)2(0.998)998]

= 0.3233

(b) By poission distribution,

expected number of guards which would be trained = 1000 * 0.002 = 2

Pr(X >=3) = Poisson (X>=3; 2) = 0.3233

(c) Yes, poisson distribution for an approximation is a perfect choice in this case. here in this case sample size is very large and probability of success is very low so in such case the approximation is good.

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