Question

Suppose that a company finds that the mean number of sick days for their employees is 5.5 days/year with a standard deviation of 2.4 days/year. What is the probability that a sample of 30 employees finds a mean of at least 6.5 days/year?

Answer #1

Let X be the random variable denoting the mean number of sick days for their employees.

So, X ~ N(5.5, 2.4^{2})

So, probability that the mean number of sick days for their employees is atleast 6.5 days =

P(X > 6.5) = 1 - P(X < 6.5)

Standardising the normal distribution

= 1 - P(Z < (6.5-5.5)/2.4)

= 1 - P(Z < 0.41667)

= 1 - 0.6615

= 0.3385.

So, the probability that a sample of 30 employees finds a mean of atleast 6.5 days per year is 0.3385.

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