Question

# . In an experiment comparing two weight loss plans, 100 subjects were randomly assigned to two...

. 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?

(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 (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.

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