Question

. In an experiment comparing two weight loss plans, 100 subjects were randomly assigned to two groups, A and B. The mean weight loss in group A was 10 pounds with a standard deviation of 8 pounds and the mean weight loss in group B was 7 pounds with a standard deviation of 11 pounds. The distributions of weight loss are approximately normal.

            a. What is the probability that a randomly selected person from group A lost weight?

            b. What is the probability that a randomly selected person from group B gained weight?

            c. If you were to randomly select 3 people from group A, what is the probability that they

                        lost a total of 25 pounds or more?

            d. If you were to randomly select one person from each group, what is the probability that

                        the person from group B lost more weight?

            e. What is the probability that a randomly selected person from group A lost at least 5 more

                        pounds than a randomly selected person from group B?

            f. In parts c-e, what assumption did you have to make? Is it reasonable?

Answer 1

(a)

Let X shows the weight loss of a person is group A. The z-score for x = 0 is

The probability that a randomly selected person from group A lost weight is

(b)

Let Y shows the weight loss of a person is group B. The z-score for Y = 0 is

The probability that a randomly selected person from group B gained weight is

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(c)

Let T= X+X+X

Here T has normal distribution with parameters as follows

and standard deviation

The z-score for T = 25 is

The probability that they lost a total of 25 pounds or more is

(d)

Let W =X -Y

Here we need to find the probability W < 0.

The distribution of W will be normal with mean

and standard deviation

The z-score for W=0 is

The probability that the person from group B lost more weight is

(e)

Let W =X -Y

Here we need to find the probability W >= 5.

The distribution of W will be normal with mean

and standard deviation

The z-score for W=0 is

The probability that a randomly selected person from group A lost at least 5 more pounds than a randomly selected person from group B

(f)

Assumption: Normal distribution

Because distribution of weight losses are normal.