Select a discrete probability distribution and present a real-life application of that distribution. Interpret the expected value and the standard deviation of your selected distribution within the context of the real-life example that you have selected, and describe how these values can be used by enterprise decision-makers.

Answers

Answer 1

Answer:

Answer:

If a new product wants to be tested by a company and decides to show 50 samples of this product to 50 selected customers. The company estimates that the probability that the customer buys the product is 0.67, the objective is to determine approximately how many people expect to buy the product.

Let X the random variable of interest "Number of people that will buy a selected product", on this case we now that:

$X \sim Binom(n=50, p=0.67)$

The expected value is given by this formula:

$E(X) = np=50*0.67=33.50$

And the standard deviation for the random variable is given by:

$sd(X)=√(np(1-p))=√(50*0.67*(1-0.67))=3.32$

So then they can conclude that for each group of 50 people they expect that about 33-34 peoploe will buy the product with a standard deviation of 3.32.

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

Solution to the problem

Let X the random variable of interest "Number of people that will buy a selected product", on this case we now that:

$X \sim Binom(n=50, p=0.67)$

The expected value is given by this formula:

$E(X) = np=50*0.67=33.50$

And the standard deviation for the random variable is given by:

$sd(X)=√(np(1-p))=√(50*0.67*(1-0.67))=3.32$

So then they can conclude that for each group of 50 people they expect that about 33-34 peoploe will buy the product with a standard deviation of 3.32.

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The State Police are trying to crack down on speeding on a particular portion of the Massachusetts Turnpike. To aid in this pursuit, they have purchased a new radar gun that promises greater consistency and reliability. Specifically, the gun advertises ± one-mile-per-hour accuracy 75% of the time; that is, there is a 0.75 probability that the gun will detect a speeder, if the driver is actually speeding. Assume there is a 1% chance that the gun erroneously detects a speeder even when the driver is below the speed limit. Suppose that 72% of the drivers drive below the speed limit on this stretch of the Massachusetts Turnpike. a. What is the probability that the gun detects speeding and the driver was speeding?
b. What is the probability that the gun detects speeding and the driver was not speeding?
c. Suppose the police stop a driver because the gun detects speeding. What is the probability that the driver was actually driving below the speed limit?

Answers

Answer:

a) P(A∩B) = 0.21

b) P(A∩B') = 0.0072

c) P(B'|A)=0.0072/0.2172=0.0331

Step-by-step explanation:

A = the gun will detect a speeder

B = driver is actually speeding

P(A|B) = 0.75

P(A|B')=0.01

P(B') = 0.72

a) by definition

P(A∩B)=P(A|B)*P(B)=0.75*(1-0.72)=0.21

b) by definition

P(A∩B')=P(A|B')*P(B')=0.01*(0.72)=0.0072

by bayes theorem

P(B'|A)=P(A|B')*P(B')/P(A)

by total probability theorem

P(A)=P(A∩B)+P(A∩B')=0.21+0.0072=0.2172

P(B'|A)=0.0072/0.2172=0.0331

Final answer:

The probabilities asked in the question are calculated using basic principles of probability: a) the probability that the radar gun detects speeding and the driver was speeding is 21%, b) the probability that the radar gun detects speeding, and the driver was not speeding is 0.72%, c) given that a driver is stopped because the radar gun detected speeding, the probability that they were actually driving within the speed limit is 3.3%.

Explanation:

The probability of a speed detection can be divided into two different categories – the probability of an accurate detection (where the driver is actually speeding), and a false detection (where the driver is not speeding).

a. The probability that the gun detects speeding and the driver was speeding is calculated by the accuracy of the gun, which is 75%, multiplied by the percentage of drivers that are actually speeding. Given that 28% of the drivers exceed the speed limit (100% - 72% safe drivers), the probability is 0.75*0.28 = 0.21 or 21%.

b. The probability that the gun detects a speeder when the driver is not speeding is calculated by multiplying the probability the gun makes an error (1%) and the chance that the driver is driving within the speed limit (72%). So, 0.01*0.72 = 0.0072 or 0.72%.

c. If the police stop a driver because the gun detects speeding, the probability that the driver was actually driving safely is calculated by taking the probability that the gun gives a false speed reading (0.72%) and dividing it by the total probability that the gun detects a speeding vehicle (accurate detection + false detection = 21% + 0.72% = 21.72%). So, 0.72 / 21.72 = 0.033 or 3.3%.

Learn more about Probability here:

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Solve this problem and identify the percent amount and base. what percent of 50 is 20?

Answers

I hope this helps you

Math Graded Assignment Unit Test, Part 2 Measures of Center and Spread(Score for Question 2: ___ of 5 points)
2. Consider the following line plot.
2
4
6
8
(a) What is the general trend of the graph?
(b) What is the median of the data? Explain.
(c) What is the mean of the data? Explain. Round to the Nearest tenth.
(d) Would the mean or median be affected more with a data point of 20? Explain.
Answer:
P

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Answer:

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Step-by-step explanation:

How to solve this?
4cos(4x)sin(10x)

Answers

Answer:

2/5 or 0.4

Step-by-step explanation:

What is the value of 10P10?

a. 3,628,800
b. 1,814,400
c. 100
d. 0

Answers

the answer is A.. I HAD THE SAME QUESTIONN]

The correct answer is A

What are five qualities of an entrepreneur that you can use to help you navigate the ""new normal ""

Answers

Answer:

Risk taking

Vision driven

Passionate

Goal oriented

Decision maker.

Step-by-step explanation:

An entrepreneur is a person who sets up a business, manages it and work towards maximizing profit.

In order to be able to navigate the "new normal", these five qualities are very essential in an entrepreneur if he/she wishes to go far.

Answer:

1. Integrity

2. Self discipline

3. Clear sense of direction

4 . Persistence

5. Action oriented and decisive

Step-by-step explanation:

1. Integrity can be define as the practice of being honest and showing a consistent and uncompromising adherence to strong moral and ethical principles and values.

2. Self discipline or Self-control, can be described as an aspect of inhibitory control, is the ability to regulate one's emotions, behavior and thought in the face of temptations and impulses.

3.. When have a clear sense if direction, we mean that person seem to have clear ideas about what they want to do or achieve.

4. When we say someone who is persistent, that person continues doing something or tries to do something in a determined but often unreasonable way.

5. Action oriented and decisive can be define as an action or actions done quickly and with confidence. How to use decisive action in a sentence.

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