Question

Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 12 million dollars and a standard deviation of 1.3 million dollars. One health care information systems company considers a quarter a "failure" if its sales level that quarter is in the bottom 20% 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 one decimal place.

Answer 1

Solution :

Given that,  

mean = = 12

standard deviation = = 1.3

Using standard normal table ,

P(Z < z) = 20%

P(Z < z) = 0.2

P(Z < -0.8420) = 0.

z = -0.8420

Using z-score formula,

x = z * +

x = -0.8420 * 1.3 + 12 = 10.9

the bottom 20% of the cutoff between quarters that are considered "failures" by that company and quarters that are 10.9 million doll