Math CentralQuandaries & Queries


Question from m.j., a student:

Slot Machines The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution.


If X is the random variable which is the number of times you win in 500 plays then X has a binomial distribution with p = 0.05 and n = 100. Your task is to find Pr( X = 30). The distribution of X can be approximated by the normal distribution with μ = np = 500 × 0.05 and σ = np(1 - p) = 500 × 0.05 × 0.95.

Pr(X = 30) where X has the binomial distribution is approximated by Pr(29.5 < X < 30.5) where X has the normal distribution. Now use the example I showed you earlier to calculate this probability.


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