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Suppose you will play 64 independent rounds of a game and have a one in five...

Suppose you will play 64 independent rounds of a game and have a one in five chance to win each round. Use a normal approximation to estimate the chance you will win at most 10 rounds.

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Answer #1

Solution:

We are given

n = 64

p = 1/5 = 0.20

q = 1 – 0.20 = 0.80

Mean = np = 64*0.20 = 12.8

SD = sqrt(npq) = sqrt(64*0.20*0.80) = 3.2

We have to find P(X≤10) = P(X<10.5) (continuity correction)

Z = (X – mean)/SD

Z = (10.5 - 12.8)/3.2

Z = -0.71875

P(Z<-0.71875) = P(X≤10) = 0.236147

(by using z-table)

Required probability = 0.236147

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