METHODS AND APPLICATIONS Assignment | College Homework Help

Exercise 5.12 METHODS AND APPLICATIONS
Suppose that the probability distribution of a random variable x can be described by the formula

Don't use plagiarized sources. Get Your Assignment on
METHODS AND APPLICATIONS Assignment | College Homework Help
Just from $13/Page
Order Now

P(x) = x
________________________________________
15College Homework Help

for each of the values x = 1, 2, 3, 4, and 5. For example, then, P(x = 2) = p(2) =2/15.

(a) Write out the probability distribution of x. (Write all fractions in reduced form.)

x 1   2   3   4   5

P(x) ________________________________________   ________________________________________   ________________________________________   ________________________________________   ________________________________________

________________________________________

(b) Show that the probability distribution of x satisfies the properties of a discrete probability distribution.(Round other answers to the nearest whole number. Leave no cells blank – be certain to enter “0” wherever required.)

P(x) ≥   for each value of x.

 

(c) Calculate the mean of x. (Round your answer to 3 decimal places.)

µx

(d) Calculate the variance, σ2x , and the standard deviation, σx. (Round your answer σx2 in to 3 decimal places and round answer σx in to 4 decimal places.)

σx2

σx

2.
award:
3.43 out of
5.00 points

Exercise 5.23 METHODS AND APPLICATIONS
Suppose that x is a binomial random variable with n = 5, p = 0.3, and q = 0.7.

(b)  For each value of x, calculate p(x), and graph the binomial distribution. (Round final answers to 5 decimal places.)

p(0) =  , p(1) =  , p(2) =  , p (3) =  ,
p(4) =  , p(5) =

(c) Find P(x = 3). (Round final answer to 5 decimal places.)

P(x=3)

(d) Find P(x ≤ 3). (Do not round intermediate calculations.  The round final answer to 5 decimal places.)

P(x ≤ 3)

(e) Find P(x < 3). (Do not round intermediate calculations. The round final answer to 5 decimal places.)

P(x < 3) = P(x ≤ 2)

(f) Find P(x ≥ 4). (Do not round intermediate calculations. The round final answer to 5 decimal places.)

P(x ≥ 4)

(g) Find P(x > 2). (Do not round intermediate calculations. The round final answer to 5 decimal places.)

P(x > 2)

(h) Use the probabilities you computed in part b to calculate the mean, μx, the variance, σ 2x, and the standard deviation, σx, of this binomial distribution. Show that the formulas for μx, σ 2x, and σx given in this section give the same results. (Do not round intermediate calculations. Round final answers to µx and σ 2x into 2 decimal places, and σx into 6 decimal places.)

µx

σ2x

σx

(i) Calculate the interval [μx ± 2σx]. Use the probabilities of part b to find the probability that x will be in this interval. Hint: When calculating probability, round up the lower interval to the next whole number and round down the upper interval to the previous whole number. (Round your answers to 5 decimal places. A negative sign should be used instead of parentheses.)

The interval is [ ,  ].

P(  ≤ x ≤  ) =

3.
award:
3 out of
3.00 points

MC Qu. 14 The mean of the binomial distribution is equ…
The mean of the binomial distribution is equal to:

p

np

(n) (p) (1-p)

px (1-p)n-x
5.
award:
3 out of
3.00 points

MC Qu. 25 A fair die is rolled 10 times. What is the p…
A fair die is rolled 10 times. What is the probability that an odd number (1, 3, or 5) will occur less than 3 times?College Homework Help

.1550

.8450

.0547

.7752

.1172
8.
award:
3 out of
3.00 points

MC Qu. 31 If n = 20 and p = .4, then the mean of the b…
If n = 20 and p = .4, then the mean of the binomial distribution is

.4

4.8

8

12
10.
award:
3 out of
3.00 points

MC Qu. 36 The probability that a given computer chip w…
The probability that a given computer chip will fail is 0.02. Find the probability that of 5 delivered chips, exactly 2 will fail.

.9039

.0000

.0922

.0038
12.
award:
3 out of
3.00 points

MC Qu. 38 In the most recent election, 19% of all elig…
In the most recent election, 19% of all eligible college students voted. If a random sample of 20 students were surveyed:
Find the probability that exactly half voted in the election.

.4997

.0014

.0148

.0000
13.
award:
3 out of
3.00 points

MC Qu. 39 In the most recent election, 19% of all elig…
In the most recent election, 19% of all eligible college students voted. If a random sample of 20 students were surveyed:
Find the probability that none of the students voted.

.0148

.4997

.0014

.0000
21.
award:
3 out of
3.00 points

MC Qu. 55 For a random variable X, the mean value of t…
For a random variable X, the mean value of the squared deviations of its values from their expected value is called its

Standard Deviation

Mean

Probability

Variance
25.
award:
3 out of
3.00 points

MC Qu. 62 If the probability distribution of X is:&nbs…
If the probability distribution of X is:

 

What is the expected value of X?

2.25

2.24

1.0

5.0

26.
award:
0 out of
3.00 points

MC Qu. 63 If the probability distribution of X is:&nbs…
If the probability distribution of X is:

 

What is the variance of X?

5.0

1.0

2.25

2.24

28.
award:
0 out of
3.00 points

MC Qu. 66 A vaccine is 95 percent effective. What is t…
A vaccine is 95 percent effective. What is the probability that it is not effective for, more than one out of 20 individuals?

.3774

.7359

.2641

.3585
P(X ≥ 2) = 1 – [P(X = 0) + p(X = 1)]
P(X ≥ 2) = 1 – [(.3585) + (.3774)] = .2641

29.
award:
3 out of
3.00 pointsCollege Homework Help

MC Qu. 67 If the probability of a success on a single …
If the probability of a success on a single trial is .2, what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

.1074

.2013

.5033

.0031

31.
award:
3 out of
3.00 points

MC Qu. 78 For a binomial process, the probability of s…
For a binomial process, the probability of success is 40% and the number of trials is 5.
Find the expected value.

5.0

1.1

1.2

2.0
E[X] = (5) (.40) = 2
32.
award:
0 out of
3.00 points

MC Qu. 79 For a binomial process, the probability of s…
For a binomial process, the probability of success is 40% and the number of trials is 5.
Find the variance.

1.1

1.2

5.0

2.0

33.
award:
3 out of
3.00 points

MC Qu. 80 For a binomial process, the probability of s…
For a binomial process, the probability of success is 40% and the number of trials is 5.
Find the standard deviation.

1.1

5.0

2.0

1.2

34.
award:
3 out of
3.00 points

MC Qu. 82 For a binomial process, the probability of s…
For a binomial process, the probability of success is 40% and the number of trials is 5.
Find P(X > 4).

.0102

.0778

.0870

.3370
P(X = 5) = (.4)5 = .0102
37.
award:
3 out of
3.00 points

MC Qu. 92 If X has the probability distribution%…
If X has the probability distribution

 

compute the expected value of X.

0.5

0.7

1.0

0.3
E[X] = -1(.2) + 0(.3) + 1(.5) = .3
38.
award:
3 out of
3.00 points

MC Qu. 93 If X has the probability distribution%…
If X has the probability distribution

 

compute the expected value of X.

1.3

2.4

1.0

1.8
E[X] = (-2) (.2) + (-1) (.2) + (1) (.2) + (2) (.2) + (9) (.2) = 1.8
40.
award:
0 out of
3.00 points

MC Qu. 95 X has the following probability distribution…
X has the following probability distribution P(X):

 

Compute the variance value of X.

1.58

.625

.850

.955
E[X] = (1) (.1) + (2) (.5) + (3) (.2) + (4) (.2) = 2.5
= (1 – 2.5)2 (.1) + (2 – 2.5)2 (.5) + (3 – 2.5)2 (.2) + (4 – 2.5)2 (.2) = .850
41.
award:
3 out of
3.00 points

MC Qu. 99 Consider the experiment of tossing a fair co…
Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads).
Determine the expected number of heads.

1.1

1.5

1.0

2.0

42.
award:
0 out of
3.00 points

MC Qu. 100 Consider the experiment of tossing a fair co…
Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads).
What is the variance for this distribution?

0.75

0.87

1.22

1.5

44.
award:
0 out of
3.00 points

MC Qu. 102 Consider the experiment of tossing a fair co…
Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads).
If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw, how much would you expect to win on average?

$6

$3

$9

$2

46.
award:
3 out of
3.00 points

MC Qu. 104 According to data from the state blood progr…
According to data from the state blood program, 40% of all individuals have group A blood. If six (6) individuals give blood, find the probability that None of the individuals has group A blood?

.0467

.4000

.0041

.0410
View Hint #1
47.
award:
3 out of
3.00 pointsCollege Homework Help

MC Qu. 105 According to data from the state blood progr…
According to data from the state blood program, 40% of all individuals have group A blood. If six (6) individuals give blood, find the probability that Exactly three of the individuals has group A blood?

.4000

.2765

.5875

.0041
48.
award:
3 out of
3.00 points

MC Qu. 106 According to data from the state blood progr…
According to data from the state blood program, 40% of all individuals have group A blood. If six (6) individuals give blood, find the probability that At least 3 of the individuals have group A blood.

.4557

.8208

.1792

.5443
P(x ≥ 3) = P(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = .4557
53.
award:
0 out of
3.00 points

MC Qu. 113 An important part of the customer service re…
An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that fewer than two troubles will be repaired on the same day?

.0010

.0146

.0156

.6328
P(x < 2) = P(x = 0) + P(x = 1) = .0156
56.
award:
0 out of
3.00 points

MC Qu. 116 The Post Office has established a record in …
The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day. If you mail eight local letters, what is the probability that all of them will be delivered the next day.

1.0

.5695

.4305

.8131
P(x = 8) = .4305
57.
award:
3 out of
3.00 points

MC Qu. 117 The Post Office has established a record in …
The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day. Of the eight, what is the average number you expect to be delivered the next day?

4.0

2.7

3.6

7.2
= np = (8) (.9) = 7.2
58.
award:
0 out of
3.00 points

MC Qu. 118 The Post Office has established a record in …
The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day. Calculate the standard deviation of the number delivered when 8 local letters are mailed.

.72

.85

2.83

2.68
Σ =  =  =  = .85
61.
award:
3 out of
3.00 points

MC Qu. 124 A large disaster cleaning company estimates …
A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that is has contracted calculate the mean number of jobs completed within the bid time.

2.0

5.6

4.0

2.4
= np = 8(.3) = 2.4
62.
award:
0 out of
3.00 points

MC Qu. 125 A large disaster cleaning company estimates …
A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that is has contracted find the probability that x (number of jobs finished on time) is within one standard deviation of the mean.

.5506

.6867

.8844

.7483
σ = √npq = 1.3. P(µ+/-σ) = P(2.4+/-1.3) = P(1.1≤X≤3.7) = P(2≤X≤3) = 0.2965+0.2541 = 0.5506 Get Business & Finance homework help today

 

Calculate your paper price
Pages (550 words)
Approximate price: -

Why Choose Us

Quality Papers

At Myhomeworkwriters.com, we always aim at 100% customer satisfaction. As such, we never compromise o the quality of our homework services. Our homework helpers ensure that they craft each paper carefully to match the requirements of the instruction form.

Professional Academic Writers

With Myhomeworkwriters.com, every student is guaranteed high-quality, professionally written papers. We ensure that we hire individuals with high academic qualifications who can maintain our quality policy. These writers undergo further training to sharpen their writing skills, making them more competent in writing academic papers.

Affordable Prices

Our company maintains a fair pricing system for all academic writing services to ensure affordability. Our pricing system generates quotations based on the properties of individual papers.

On-Time delivery

My Homework Writers guarantees all students of swift delivery of papers. We understand that time is an essential factor in the academic world. Therefore, we ensure that we deliver the paper on or before the agreed date to give students ample time for reviewing.

100% Originality

Myhomeworkwriters.com maintains a zero-plagiarism policy in all papers. As such, My Homework Writers professional academic writers ensure that they use the students’ instructions to deliver plagiarism-free papers. We are very keen on avoiding any chance of similarities with previous papers.

Customer Support 24/7

Our customer support works around the clock to provide students with assistance or guidance at any time of the day. Students can always communicate with us through our live chat system or our email and receive instant responses. Feel free to contact us via the Chat window or support email: support@myhomeworkwriters.com.

Try it now!

Calculate the price of your order

You will get a personal manager and a discount.
We'll send you the first draft for approval by at
Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Homework Writing Services

My Homework Writers holds a reputation for being a platform that provides high-quality homework writing services. All you need to do is provide us with all the necessary requirements of the paper and wait for quality results.

Essays

Essay Writing Services

At My Homework Writers, we have highly qualified academic gurus who will offer great assistance towards completing your essays. Our homework writing service providers are well-versed with all the aspects of developing high-quality and relevant essays.

Admissions

Admission and Business Papers

With Myhomeworkwriters.com, we will help you secure a position at your desired institution. Our essay writing services include the crafting of admissions papers. We will still help you climb your career ladder by helping you write the official papers that will help you secure a job. We will guide you on how to write an outstanding portfolio or resume.

Editing

Editing and Proofreading

Myhomeworkwriters.com has a professional editorial team that will help you organize your paper, paraphrase it, and eliminate any possible mistakes. Also, we will help you check on plagiarism to ensure that your final paper posses quality and originality.

Coursework

Technical papers

My Homework Writers harbors professional academic writers from diverse academic disciplines. As such, we can develop homework writing services in all academic areas. The simplicity or complexity of the paper does not affect the quality of homework writing services.