Suppose that there are fifteen employees in an office, and each employee would l

Question

Suppose that there are fifteen employees in an office, and each employee would like a new computer with probability 0.6. Each employee is independent of the others. Suppose that the office manager would like to purchase enough computers such that it is very likely that all employees wanting new computers will receive them, while also keeping costs manageable. To help the manager explore their options, find the smallest integer k such that P(X > k) 0.05 when X is a random variable counting the number of employees who want new computers (i.e., k is the smallest number of computers that has at least a 95% likelihood of providing new computers to all employees wanting them).

Explanation / Answer

Here it is binomial distribution with p=0.6 and n=15

Now using online binomial calculator we get P(x>8)=0.61 and P(x>9)=0.40

So the required number k is 9.

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