Question

You roll a fair die 5 times. What is the probability you get at least four...

You roll a fair die 5 times. What is the probability you get at least four 6’s? This time you roll the die 204 times. What is the probability you get between 30 and 40 6’s?

Homework Answers

Answer #1

Binomial distribution: P(X) = nCx px qn-x

P(at least four 6's in 5 rolls) = P(4) + P(5) + P(6)

= 6C4x(1/6)4(5/6)2 + 6C5x(1/6)5x(5/6) + (1/6)6

= 0.0080 + 0.0006 + 0.0001

= 0.0087

Norml approximation for binomial distribution

n = 204

p = 1/6

q = 5/6

Mean = np = 34

Standard deviation = = 5.323

P(X < A) = P(Z < (A - mean)/standard deviation)

P(between 30 and 40 6’s) = P(X < 40.5) - P(X < 29.5) (continuity correction of 0.5 applied)

= P(Z < (40.5 - 34)/5.323) - P(Z < (29.5 - 34)/5.323)

= P(Z < 1.22) - P(Z < -0.85)

= 0.8888 - 0.1977

= 0.6911

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