Suppose that the quarterly sales levels among health care in

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

Solution

Everything is based on normal distribution so just go ahead and solve turning everything over to a N(0,1)

Probability ( Z< ( x-8 million)/1.1 million) =.15

You want the x value that meets the .15 or 15% level and you have transformed your data into N(0,1)

Therefore we have (x-8mil)/1.1mil = -1.0364

Now just solve for x

x= -1.0363(1.1mil) + 8 mil = 8 mil - 1.1399 mill
====> 6.8601 million

with rounding I would go with 6.86 milliion

This company would assume a failure if they had sales below the 6.86 million dollar level