How JustAnswer Works:

  • Ask an Expert
    Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.
  • Get a Professional Answer
    Via email, text message, or notification as you wait on our site.
    Ask follow up questions if you need to.
  • 100% Satisfaction Guarantee
    Rate the answer you receive.

Ask Chirag Your Own Question

Chirag
Chirag, Master's Degree
Category: Calculus and Above
Satisfied Customers: 12191
Experience:  I have a Master's degree in Engineering and a very wide teaching experience of more than 25 years at various levels.
13269833
Type Your Calculus and Above Question Here...
Chirag is online now
A new question is answered every 9 seconds

Create an example probability distribution to the right in

Resolved Question:

Create an example probability distribution to the right in which the expected value is 15. You must have at least three different values for x.

What are the values for the mean and standard deviation of a standard normal distribution?
What are considered unusual z-score values?

The serum cholesterol levels in milligrams/deciliter (mg/dL) in a certain Mediterranean population are found to be normally distributed with a mean of 160 and a standard deviation of 50. Answer the following:

(a) Determine the z-score for a person from this population that has a cholesterol level of 115. Then find the z-score for someone whose cholesterol level is 242.
(b) If x represents a possible cholesterol level from this population, find P(x > 145).

(c) Find P(100 < x < 200) and give an interpretation of this value.

(d) The top 3% of all people in this group have cholesterol levels that make them "at-risk" for heart problems. Determine the raw-score cholesterol level which separates the at-risk people from the rest of the group.

Does a confidence interval for µ get wider or narrower if:
(a) the percent of desired confidence (confidence level) decreases from 99% to 90%?

(b) the size of the sample used to produce the confidence interval is decreased?
(c) our estimate of the standard deviation gets smaller?
Submitted: 11 months ago.
Category: Calculus and Above
Expert:  Chirag replied 11 months ago.
Hi, Welcome and Thanks for using Just Answer

I will assist you with these. I am working on this and will post the answers as soon as ready.

Thanks.
Customer: replied 11 months ago.


ok... do you have an idea of how long it may take?

Expert:  Chirag replied 11 months ago.
It may take a maximum of one hour. Is that ok?
Customer: replied 11 months ago.


That's fine, just need it in no more than an hour and a half

Expert:  Chirag replied 11 months ago.
Sure.
Expert:  Chirag replied 11 months ago.
Here are the answers ...

(1)

Let the x- values be 3, 15, 25, 23 and the corresponding probabilities be 0.3, 0.3, 0.2, 0.2

The probability distribution is
x P(x)
3 0.3
15 0.3
25 0.2
23 0.2

(2)

Mean = 0 and Standard deviation = 1
z- scores less than -2 or greater than 2 are considered unusual

(3)

z = (x – μ)/σ
(a) For x = 115, z = (115 – 160)/50 = -0.90 and
for x = 242, z = (242 – 160)/50 = 1.64

(b) For x = 145, z = (145 – 160)/50 = -0.30
P(x > 145) = P(z > -0.30) = 0.618

(c) For x = 100, z = (100 – 160)/50 = -1.2 and
for x = 200, z = (200 – 160)/50 = 0.80
P(100 < x < 200) = P(-1.2 < z < 0.8) = 0.673
This means the probability of finding a person from the population with cholesterol level between 100 and 200 is 0.673

(d) The upper-tail z- score for 3% (0.03) is 1.881
x = μ + z * σ = 160 + 1.881 * 50 = 254.05

(4)

(a) The confidence interval gets narrower if the confidence level is decreased from 99% to 90%

(b) The confidence interval gets wider if the sample size is decreased

(c) The confidence interval gets narrower if the standard deviation gets smaller



I hope that helps. Please Rate My Answer (Tip If Happy).

Thanks.
Chirag, Master's Degree
Satisfied Customers: 12191
Experience: I have a Master's degree in Engineering and a very wide teaching experience of more than 25 years at various levels.
Chirag and other Calculus and Above Specialists are ready to help you
Customer: replied 11 months ago.


could you elaborate on 1? How did you get those values?

Expert:  Chirag replied 11 months ago.
(1)

We want the expected value to be 15. The expected value is given by the formula ∑(x * P(x)). So, we choose four values in such a way that when they are multiplied with the respective assumed probabilities, and the products added, the result should be 15. I did that and got four values of x as 3, 15, 25 and 23.

(2)

The normal distribution is defined by two parameters, μ and σ.
For the standard normal distribution, the values of μ and σ are respectively μ = 0 and σ = 1 (These are standardized values, and are fixed).

Area under the normal curve gives the probabilities. Area to the left of z = -2 is 0.0228 and area to the right of z = 2 is also 0.0228. This means the probability is just 2.3% for z- values less than -2 or greater than 2. Since this probability is low, z 2 is considered unusual range.


I hope that helps. Please Rate My Answer (Tip If Happy).

Thanks.



JustAnswer in the News:

 
 
 
Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.
JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.
Web sites like justanswer.com/legal
...leave nothing to chance.
Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.
Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.
I will tell you that...the things you have to go through to be an Expert are quite rigorous.
 
 
 

What Customers are Saying:

 
 
 
  • Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
< Last | Next >
  • Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
  • This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!! Alex Los Angeles, CA
  • Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult. GP Hesperia, CA
  • I couldn't be more satisfied! This is the site I will always come to when I need a second opinion. Justin Kernersville, NC
  • Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around. Esther Woodstock, NY
  • Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know. Robin Elkton, Maryland
  • He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here. Diane Dallas, TX
 
 
 

Meet The Experts:

 
 
 
  • SusanAthena

    Master's Degree

    Satisfied Customers:

    98
    Tutor for Algebra, Geometry, Statistics. Explaining math in plain English.
< Last | Next >
  • http://ww2.justanswer.com/uploads/homeworklady/2008-11-24_125231_susannewavatar.jpg SusanAthena's Avatar

    SusanAthena

    Master's Degree

    Satisfied Customers:

    98
    Tutor for Algebra, Geometry, Statistics. Explaining math in plain English.
  • http://ww2.justanswer.com/uploads/ED/educatortech/2012-6-7_1256_williams4.64x64.jpg Mr. Gregory White's Avatar

    Mr. Gregory White

    Master's Degree

    Satisfied Customers:

    93
    M.A., M.S. Education / Educational Administration
  • http://ww2.justanswer.com/uploads/CO/CosumelEyes/2012-5-4_4923_Profile.64x64.jpg Ray Atkinson's Avatar

    Ray Atkinson

    Bachelor's Degree

    Satisfied Customers:

    45
    Degrees in Math, Education and Accounting, years and years of tutoring.
  • http://ww2.justanswer.com/uploads/SO/sonofGauss/2012-6-6_20151_PortraitLHW.64x64.jpg JACUSTOMER-yrynbdjl-'s Avatar

    JACUSTOMER-yrynbdjl-

    Master's Degree

    Satisfied Customers:

    42
    I have a MS in Mathematics and I have taught Mathematics for 10 years at the college level.
  • http://ww2.justanswer.com/uploads/dhouse1940/2010-09-02_133023_DSCN2406.jpg dhouse1940's Avatar

    dhouse1940

    Master's Degree

    Satisfied Customers:

    33
    BS mathematics, MS biostatistics, 35+ yrs designing & analyzing biological experiments.
  • http://ww2.justanswer.com/uploads/AR/arubin9/2012-2-4_42617_ArthurRubinedit.64x64.jpg Dr Arthur Rubin's Avatar

    Dr Arthur Rubin

    Doctoral Degree

    Satisfied Customers:

    32
    Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers
  • http://ww2.justanswer.com/uploads/DO/Donbacongamer/2012-3-6_2337_mathmaster.64x64.jpg Don's Avatar

    Don

    Master's Degree

    Satisfied Customers:

    29
    M.S. Astronautical Engineering. Math/Sci/Comp Tutor