Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 10 million dollars and a standard deviation of 1.1

Question

Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed with a mean of 10

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 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

x = sales level in millions

z statistic = (x - mean)/standard deviation

first find z-statistic the corresponds to 20th percentile.(-0.84)

we are given mean is 10 and standard deviation is 1.1

plug those values into z-statistic equations and solve for x:

-0.84 = (x - 10)/1.1 = 8.824