Michael reaches into a very large box and pulls out Lucky Charms. If percentages

Question

Michael reaches into a very large box and pulls out Lucky Charms. If percentages of the pieces are: 50% regular cereal, 6.25% each for hearts, starts, horseshoes, clovers, blue moons, pots of gold, rainbows, and red balloons, and he only wants blue moons. Let X be the number of individual pieces he has to pull out until he gets a blue moon including the blue moon.

h) What is the expected number of the number of pieces that he has to pull out to get his first blue moon?

i) What is the standard deviation of the number of pieces has to pull out to get his first blue moon?

Explanation / Answer

P(blue moons), p = 0.0625

This is a geometric distribution

a) expected value = 1/p

                          = 1 / 0.0625

                          = 16

b) Variance = (1 - p) / p2

                 = (1 - 0.0625) / 0.06252

                 = 240

standard deviation = sqrt(240) = 15.49 or 15 (approx.)

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