New Process Inc. a large mail-order supplier of women's fashions, advertises same-day service upon every order. Currently the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the technique of order handling. The goal is to have fewer than 4 unfilled orders on hand at the end of 90 percent of the working days. Frequent checks of the unfilled orders at the end of the day reveal that the distribution of the unfilled orders follows a Poisson distribution with a mean of 2.6 orders.
(a) Has New Process Inc. lived up to its internal goal? (Round your answer to 5 decimal places.)
P(X < 4 | µ = 2.6)