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

(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.

A study was conducted in order to compare the weight loss for
two diet plans, Plan A and Plan B. Two hundred dieters were
randomly selected. Of this sample 100 were placed on the Plan A
diet and the remaining 100 were assigned to the Plan B diet. After
the dieters were on the diet for 2 months the average weight loss
and sample standard deviation of the weight losses were recorded.
For the Plan A group there was an...

Are low-fat diets or low-carb diets more effective for weight
loss? A sample of 46 subjects went on a low-carbohydrate diet for
six months. At the end of that time, the sample mean weight loss
was 4.6 kilograms with a sample standard deviation of 6.28
kilograms. A second sample of 49 subjects went on a low-fat diet.
Their sample mean weight loss was 2.3 kilograms with a standard
deviation of 4.66 kilograms. Can you conclude that the mean weight
loss...

You have joined a small drug
manufacturer. They have developed a weight loss pill. In general
people do not lose weight. That is, the weight change of an adult
for any 6-month period would average zero. With these “pills” for
this sample of 20 people they appear to be losing weight. The
weight change is in the table at the end of this test. A plus means
the person lost weight, a minus means the person gained weight. You
are...

A, Eighteen subjects were randomly selected and given
proficiency tests. the mean of this group is 492.3 and the standard
deviation is 37.6. Construct the 95% confidence interval for the
population mean.
B, use the sample data given in the above problem to construct
the 98% confidence interval for the population standard
deviation.

Are low-fat diets or low-carb diets more effective for weight
loss? A sample of 70 subjects went on a low-carbohydrate diet for
six months. At the end of that time, the sample mean weight loss
was 10.5 pounds with a sample standard deviation of 7.09 pounds. A
second sample of 76 subjects went on a low-fat diet. Their sample
mean weight loss was 18.0 with a standard deviation of 7.26. Can
you conclude that their was no difference in the...

are low fat diets or low carb diets more effective for weight
loss? a sample of 70 subjects went on a low carbohydrate diet for 6
months. a the end of that time, the sample mean weight loss was
10.5 pounds with a sample standard deviation of 7.09 pounds. a
second sample of 76 subjects went on a low fat diet. their sawith a
sample mean weight loss was 18.0 with a standard deviation of 7.26.
test the claim that...

The producer of a weight-loss pill advertises that people who
use the pill lose, after one week, an average (mean) of 1.8 pounds
with a standard deviation of 0.95 pounds. In a recent study, a
group of 60 people who used this pill were interviewed. The study
revealed that these people lost a mean of 1.73 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...

A weight-loss company wants to make sure that it's clients lose
more weight, on average, than they would without the company's
help. An independent researcher collects data on the amount of
weight lost in one month from 45 of the company's clients and finds
a mean weight loss of 12 pounds. The population standard deviation
for the company's clients is known to be 7 pounds per month. Data
from 50 dieters not using the company's services reported a mean
weight...

X is a random variable for the weight of a steak. The
distribution of X is assumed to be right skewed with a mean of 3.5
pounds and a standard deviation of 2.32 pounds.
1. Why is this assumption of right skewed reasonable?
2. Why cant you find the probability that a randomly chosen
steak weighs over 3 pounds?
3. 5 steaks randomly selected, can u determine the probability
that the average weight is over 3 pounds? Explain.
4. 12...

In a large-scale experiment, a researcher randomly assigned
6,000 subjects to receive either a drug or a placebo. 4,000
patients were assigned to receive the drug, and the other 2,000
patients received the placebo. The researcher did a quick headcount
in the drug-receiving group and noted that there were 3,002 males
who received the drug. The researcher does not have time to do a
headcount in the placebo group. Which is the most reasonable number
of males in the placebo...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 43 seconds ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 6 minutes ago

asked 11 minutes ago

asked 12 minutes ago

asked 16 minutes ago

asked 16 minutes ago

asked 17 minutes ago

asked 17 minutes ago