Question

For this discussion, consider how probability is used in real world scenarios and how they can be solved.

**Post** a real world probability problem for your
classmates to solve. Use normal or binomial distribution within the
problem.

Answer #1

One of real world probability problem is weather forecasting. We can see in any weather forecasting sites, there is an information of probability of rain on any particular day or in any particular time period. We use that information to plan our outdoor activities. Let's say that on average based on past data, it will rain on 12 days in the month of September. Thus, the probability of rain on any given particular day in September month is 12/30 = 0.4. Suppose I need to go for a extra classes this whole week (7 days). Let X be the number of days in the week, I expect a rainy day. Then X ~ Binomial(n = 7, p = 0.4)

The problems based on this scenario can be,

What is the probability that I encounter no rainy days in that week?

Ans. P(X = 0) = ^{7}C_{0} * 0.4^{0} * (1
- 0.4)^{7} = 0.0279936

What is the probability that I encounter 3 rainy days in that week?

Ans. P(X = 3) = ^{7}C_{3} * 0.4^{3} * (1
- 0.4)^{4} = 0.290304

What is the expected number of rainy days in a week?

Ans. E(X) = np = 7 * 0.4 = 2.8 days

If today is a rainy day, what is the chance that tomorrow is also a rainy day?

Ans. Since we assume in a Binomial distribution, that all days are independent, the probability of rain next day is independent of today and is equal to p = 0.4

Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.n
equals 54. p equals 0.7. X equals 46. Use the binomial probability
formula to find P(X).
Can the normal distribution be used to approximate this
probability?
Approximate P(X) using the normal distribution. Use a standard
normal distribution table.
By how much do the exact...

Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.
n=50, p=0.50, and x=17 For n=50, p=0.5, and X=17, use the
binomial probability formula to find P(X).
Q: By how much do the exact and approximated probabilities
differ?
A. ____(Round to four decimal places as needed.)
B. The normal distribution cannot be used.

WEEK 3 DISCUSSION ("YOU CAN FOOL ALL THE PEOPLE SOME OF THE
TIME, AND SOME OF THE PEOPLE ALL OF THE TIME, BUT YOU CAN'T FOOL
ALL THE PEOPLE ALL THE TIME") BUT, LET'S TRY. YOU COME UP WITH A
PROBLEM FOR YOUR CLASSMATES TO SOLVE INVOLVING THE ADDITION RULE,
MULTIPLICATION RULE, PERMUTATIONS (WITH OR WITHOUT REPLACEMENT), OR
COMBINATIONS (WITH OR WITHOUT REPLACEMENT). HOWEVER, THE PROBLEM
YOU POST IS ALSO ONE OF YOUR HOMEWORK PROBLEMS AND YOU MUST GIVE
ITS...

Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.
nequals54, p equals 0.7, and X equals 37 For n equals 54,
pequals0.7, and Xequals37, use the binomial probability formula
to find P(X).

Now that you have had a chance to review the content covered so
far, take a moment to reflect upon what you have learned and post
in this discussion board below. Consider one or two of the
following statements in your post: Provide a real life
example that pertains to Chapter 7. Why do you think the
normal distribution is essential in the study of statistics? How
might the normal distribution apply to your program? Be ready to
comment on...

Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.
n=6060, p=0.20.2, X=25
Can the normal distribution be used to approximate this
probability?
A. Yes, the normal distribution can be used because np(1−p) ≥
10.
B. No, the normal distribution cannot be used because np(1−p)
< 10.
C. No, the normal distribution cannot be...

11.
Part A:
Create a real world (business) application and identify at least
2 random variables xi that can be approximated by the
binomial probability distribution. (at-least 100
words).
Your answer. <Be as descriptive about your
application as you can>.
Part B: Show that each that xi is a binomial random
variable by checking each of the four characteristics.

Compute P(X) using the binomial probability formula. Then
determine whether the normal distribution can be used to estimate
this probability. If so, approximate P(X) using the normal
distribution and compare the result with the exact probability.
nequals44, pequals0.4, and Xequals19 For nequals44, pequals0.4,
and Xequals19, use the binomial probability formula to find P(X).
nothing (Round to four decimal places as needed.) Can the normal
distribution be used to approximate this probability? A. No,
because StartRoot np left parenthesis 1 minus...

Consider some of the examples you have brought up in earlier
discussion forums about applying models to real-world problems.
Choose one of the models covered earlier in the course and describe
the key differences in solving a problem with that model versus
with a simulation model. In your opinion, which is more effective?
How does the problem at hand determine which type of model to
use?

Consider a binomial experiment with 16 trials and probability
0.65 of success on a single trial.
(a) Use the binomial distribution to find the probability of
exactly 10 successes. (Round your answer to three decimal
places.)
(b) Use the normal distribution to approximate the probability
of exactly 10 successes. (Round your answer to three decimal
places.)

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