Question

**In a certain county, 27% of the residents are
overweight. Choose 3 residents at random. Let X= the number of
overweight residents in the sample.**

**Find the probability all three residents in the sample are overweight (Find P(X=3) ).**

**Find the probability none of the three residents in the sample are overweight (Find P(X=0) ).**

**What are the valid values for X?**

**There are eight possible arrangements for the sample of three where 0=overweight N=not overweight. For example (O,O,O) means all three are overweight. (N,O,O) means that the first person is not overweight but the second and third residents are overweight. List all eight arrangements.**

**Find the probability of each arrangement. (They are not all equally likely) and check that the probabilities add to one.**

**Find the P(X=0), P(X=1), P(X=2), P(X=3) using your answers above.****Graph the probability distribution of X. (X on x axis and Probability on the y axis).**

**Find the E(X).**

Answer #1

A random variable X has its probability function given by
x
0
1
2
3
4
f(x)
0.3c
0.1c
c
0.2c
0.4c
a) Find c and F(x), the cumulative distribution function for X
(for all real values of X).
b) Find the probabilities of the event X = 6 and the event X
>= 4.
c) Find P(1 < X <= 4) and P(1 < X <= 4 | X <=
3).

1. Choose the two conditions that verify a table of relative
frequencies is a probability model.
Select one or more:
a. The sum of the probabilities for all of the possible outcomes
is less than 1.
b. The sum of the probabilities for all of the possible outcomes
equals 1 (or 100%).
c. There is at least one zero probability for an event.
d. All of the probabilities for the possible outcomes are at
least zero and no larger than...

1. Let x be a continuous random variable. What is the
probability that x assumes a single value, such as a (use numerical
value)?
2. The following are the three main characteristics of a normal
distribution.
The total area under a normal curve equals _____.
A normal curve is ___________ about the mean. Consequently, 50%
of the total area under a normal distribution curve lies on the
left side of the mean, and 50% lies on the right side of...

1. Groups of adults are randomly selected and arranged in groups
of three. The random variable x is the number in the group who say
that they would feel comfortable in a self-driving vehicle.
Determine whether a probability distribution is given. If a
probability distribution is given, find its mean and standard
deviation. If a probability distribution is not given, identify the
requirements that are not satisfied.
x P(x)
0 0.355
1 0.434
2 0.187
3 0.024
a.) Does the...

1.Let X be a binomial random variable with mean 9 and
variance 4.5. Find P(X = 9). ( )
2.,A wildlife biologist examines frogs for a genetic
trait that may possibly be linked to industrial toxins in the
environment. This trait is usually found in 1 of every 7 frogs, so
the prevalence is 0.143. A sample of 92 frogs are collected and
examined. (Enter all probabilities with 3
decimal points.) What is the probability that at least 9 frogs
in...

Let x be a random variable that represents white blood
cell count per cubic milliliter of whole blood. Assume that
x has a distribution that is approximately normal, with
mean μ = 6950 and estimated standard deviation σ
= 2950. A test result of x < 3500 is an indication of
leukopenia. This indicates bone marrow depression that may be the
result of a viral infection.
(a) What is the probability that, on a single test, x
is less than...

Groups of adults are randomly selected and arranged in groups of
three. The random variable x is the number in the group who say
that they would feel comfortable in a self-driving vehicle.
Determine whether a probability distribution is given. If a
probability distribution is given, find its mean and standard
deviation. If a probability distribution is not given, identify
the requirements that are not satisfied
x
P(x)
0
0.351
1
0.427
2
0.200
3
0.022
Does the table...

Obesity and being overweight is caused by excessive
adipose tissues, or body fat. Visceral fat, surrounding internal
organs, is clearly associated with heart disease and diabetes.
Subcutaneous fat, found just below the skin, often in the buttocks
and thighs, is not. A study examined the impact of exercise type on
visceral and subcutaneous fat. Overweight, sedentary, but otherwise
disease‑free adults were randomly assigned to three exercise
regimens for eight months, aerobic training, resistance training,
and aerobic plus resistance training. All...

Let x be a random variable representing dividend yield of bank
stocks. We may assume that x has a normal distribution with σ =
1.8%. A random sample of 10 bank stocks gave the following yields
(in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample
mean is x bar = 5.38%. Suppose that for the entire stock market,
the mean dividend yield is μ = 4.7%. Do these data indicate that
the dividend yield of...

I. Solve the following problem:
For the following data:
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6 n = 12
b) Calculate
1) the average or average
2) quartile-1
3) quartile-2 or medium
4) quartile-3
5) Draw box diagram (Box & Wisker)
II. PROBABILITY
1. Answer the questions using the following
contingency table, which collects the results of a study to 400
customers of a store where you want to analyze the payment
method.
_______B__________BC_____
A...

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