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 55 people who used this pill were interviewed. the study revealed that these people lost a mean of 1.95 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 1.95 pounds or less? carry your intermediate computations to at least four decimal places. round your answer to at least three decimal places.

Answer 1

To find the probability that the mean weight loss after one week on the pill for a random sample of 55 individuals will be 1.95 pounds or less, we can use the z-score formula.

Step-by-step explanation:

To find the probability that the mean weight loss after one week on the pill for a random sample of 55 individuals will be 1.95 pounds or less, we can use the z-score formula.

The z-score formula is z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, x = 1.95 pounds, μ = 1.85 pounds, σ = 0.95 pounds, and n = 55.

Calculating the z-score:

z = (1.95 - 1.85) / (0.95 / √55)

z = 0.1 / (0.1366)

z = 0.7312

Using a standard normal distribution table or a calculator, we can find that the probability of obtaining a z-score of 0.7312 or less is approximately 0.7663.

Therefore, the probability that the mean weight loss after one week on the pill for a random sample of 55 individuals will be 1.95 pounds or less is approximately 0.7663.