Question

The manager of a departmental store is thinking about establishing a new billing system for the stores credit customers. After a thorough financial analysis, she determines that the new system will not be cost effective if the average monthly account is less than 70,000. A random sample of 200 monthly accounts is drawn, for which the mean monthly account is Sh. 66,000. With  = 0.05, is there sufficient evidence to conclude that the new system will not be cost effective? Assume that the population standard deviation is Sh. 30,000

Answer 1

$\sigma_{200}=\frac{30000}{\sqrt{\smash[b]{200}}}=2121.32$

$z=\frac{70000-66000}{2121.32}=1.89$

$1-P(z)=1-0.9706=0.0294$

The project pays off with probability 2.94%