The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.75 pounds with a standard deviation of 1.02 pounds. In a recent study, a group of 55 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.83 pounds after one week. If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of 55 individuals will be 1.83 pounds or less?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.