Bob's Ice Cream Emporium has expanded into a market with only 12 possible customers and the probability that one of the 12 people goes to Bob's is 0.55. How many stools does Bob need to provide so that the chance of running short on any given day is less than 10%? Please show your work.
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it is easier to take NOT going to bob's as p = 0.45 in the binomdist
0 C(12,0) * 0.45^0 * 0.55^12 0.00077
1 C(12,1) * 0.45^1 * 0.55^11 0.00752
2 C(12,2) * 0.45^2 * 0.55^10 0.03386
3 C(12,3) * 0.45^3 * 0.55^09 0.09233
it'll be clear from the above that if the absentees are >=3, P(short) <10%
so 7 chairs need to be provided
0 C(12,0) * 0.45^0 * 0.55^12 0.00077
1 C(12,1) * 0.45^1 * 0.55^11 0.00752
2 C(12,2) * 0.45^2 * 0.55^10 0.03386
3 C(12,3) * 0.45^3 * 0.55^09 0.09233
it'll be clear from the above that if the absentees are >=3, P(short) <10%
so 7 chairs need to be provided