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 1.05 pounds. In a recent study, a group of 50 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.7 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 50 individuals will be 1.7 pounds or less? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. e х ?

Answer 1

Solution;
Given that,

μ =1.85 pounds,

σ=1.05,

n =50
For a random sample of size n= 50, sample mean is equal to the population mean
i.e. μx̄ = μ =1.85

and
sample standard deviation can be calculated as
σx̄=σ/(√n)

=1.05/(√50)

= 0.1485
P(x̄<=1.7)
=p{[(x̄- μx̄ )/σx̄]<=[(1.7 - 1.85)/0.1485]}
=P(z<= -1.01)
=0.1562

= 0.156 .......(3 decimal place)