Suppose that the quarterly sales levels among health care information systems co

Question

Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of

9

million dollars and a standard deviation of

1.1

million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom

10%

of all quarterly sales levels. Determine the sales level (in millions of dollars) that is the cutoff between quarters that are considered "failures" by that company and quarters that are not. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Explanation / Answer

Mean = 9 millions dollars

Standard deviation = 1.1 million dollars

Let A be the cutoff between quarters that are considered "failures" by that company and quarters that are not

P(X < A) = 0.1

P(X < A) = P(Z < (A - mean)/standard deviation) = 0.1

P(Z < (A - 9)/1.1) = 0.1

From standard normal distribution table, z value corresponding to probability of 0.1 can be obtained. Then,

(A-9)/1.1 = -1.28

A = 7.59

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