Question

The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of 1.85 pounds with a standard deviation of 0.95 pounds. In a recent study, a group of 45 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.77 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 45 individuals will be 1.77 pounds or less? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer 1

SOLUTION:

From given data,

An average (mean) of 1.85 pounds with a standard deviation of 0.95 pounds. In a recent study, a group of 45 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.77 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 45 individuals will be 1.77 pounds or less?

Average (mean) = = 1.85

Standard deviation = = 0.95

mean = = 1.77

= 45

So the probability is

P(x <1.77)

P(x <1.77) = P(( - ) / (/ sqrt(n) < (1.77-1.85)/(0.95 /sqrt(45)))

P(x <1.77) = P ( Z < (1.77-1.85)/(0.95 /sqrt(45)))

P(x <1.77) = P(Z < -0.56)

P(x <1.77) = 0.287    (from standard normal table)