Quantitative Methods II

The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500.
a. What is the random variable?
b. The mayor of Daisy City makes $2250 a month. What percentage of Daisy City's residents has incomes that are more than the mayor?
c. Individuals with incomes of less than $1985 per monthe are exempt from city taxes. What percentage of residents is exempt from city taxes.
d. What are the minimum and the maximum incomes of the middle 95% of the residents
e. Two hundred residents have incomes of at least $4440 per month. What is the population of Daisy City.

  1. 👍 0
  2. 👎 0
  3. 👁 1,445
  1. You have a normal distribution table handy. I do not so all I can do is outline the methods.
    mean = 3000
    sigma = 500
    a. the monthly income
    b. how far below mean is the mayor's income?
    3000 - 2250 = 750
    then how many sigmas below mean is this?
    750/500 = 1.5 sigma (called "z") below mean
    so now the question becomes how what percent of a normal distribution is between 1.5 sigma (called "z") below mean and + infinity
    this is of course 100% - the percent between -oo and 1.5 sigma below mean
    My guess not having the table handy is about 7% for between -oo and mean -1.5 sigma
    so about 93 % have more income

    c. 3000 - 1985 = 1015 below mean
    1015/500 = 2.03 sigma below mean
    look for between -oo and -2.03
    This is tiny, around 2 1/2 percent if I had a table

    d. middle 95% is from about F(z) = 2.5% to F(z)=97.5% or F(z) = .025 to .975

    That would be from about mean -2 sigma to mean + 2 sigma (use table of z versus F(z) of course. Do not trust my guess)
    so from mean -2*500 to mean + 2*500
    or from $2000 to $4000

    4440 - 3000 = 1440
    1440/500 = 2.88 sigma above mean
    so what percent below mean + 2.88 sigma?
    F(z)about .995 (remember guessing
    .005 or about .5% have incomes above 4440
    .005 n = 200
    n = 200/.005 = 40,000
    remember I am beign very approximate guessing normal distribution table.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    The deductions from Jennifer Miller’s monthly pay are federal income tax (FIT) of $87, state income tax (SIT) of 2.5% of gross, city income tax (CIT) of 1.2% of gross, Social Security, and Medicare.Her monthly next pay is

  2. math

    Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $180 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the

  3. History

    1. Which elected officials have the most power in county government? A. managers B. magistrates C. commissioners*** D. voter registration workers 2. Which of the following correctly orders municipal governments from smallest to

  4. Math, Probability

    According to a survey of Australian households, the probability that annual household income is over $50,000 if the residents own 2 cars is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The

  1. gulf model

    anil spent1/4 of his income on food 2/5 donated 1/6 on other expenses if he was left with 10000. find his monthly income

  2. Mathematics

    Raman spends 2/5 of his monthly income on food and 3/8 of the remaining on clothes. Find (a) What fraction of his income is left with him. (b) If the money left is ₹2400, find monthly income.

  3. Math/ Statistics

    The owner of a football team claims that the average attendance at home games is over 3000, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been

  4. algebra

    In 2000, 49% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.3% per year since then. Find a linear function in slope-intercept form that

  1. math

    If your annual income is $50,000 and your income share is 15%, how much is your monthly payment amount? (Feel free to use a calculator, if needed.)

  2. SS again please help me asap

    Who was most likely to participate in a corn husking? Low Country residents Up Country residents house servants plantation owners All of the following statements about South Carolina society in the late 18th century are true

  3. Math

    Ben recently purchased a new home. In order to be able to afford the home, he came up with a budget that breaks down his monthly income as follows; 30% for housing, 20% for food, 22% for utilities, 10% for savings, 6% for

  4. Pre-Calculus

    A local salesman receives a base salary of 675 monthly. He Also receives a commission of 11% on all sales over 1900. How Much would he have to sell in a month if he needed to have a monthly income of 3000? My Work: 1900*.11=209

You can view more similar questions or ask a new question.