statistics

at a bank, account balances are nomrally distribued with a mean of $637.52 and standard deviation of $623.16. What is the probability that a simple randon same of 400 accounts has mean that exceeds $1650.00? show me steps and calculations i urgently need help

  1. πŸ‘ 0
  2. πŸ‘Ž 0
  3. πŸ‘ 41
asked by son
  1. I think you either have a typo or the problem wanted to be out of reasonable range. Are you sure not $650, not $1650 ???
    Anyway here is a method:
    Sample Mean also has normal distribution
    The mean will have the same mean as the original.
    However the sigma = original sigma /sqrt(sample size) = 623.16/20
    = 31.15
    So
    The real question is in a normal distribution with mean = 637.52 and sigma = 31.15 what is the probability of over 1650?
    how far above mean? (1650 - 637.52) = 1012.48
    how many sigmas above mean?
    1012.48 / 31.15 = 32.5 sigmas from mean
    That is off any table of normal distribution. It is so improbable that the online normal distribution calculators just return zero.
    So, lets see what the probability is of the opposite, the mean lying between 0 and 32.5 sigma. It is of course .5
    In other words the probability of the sample being beyond 32.5 sigma is so tiny the calculators will not do it.

    1. πŸ‘ 0
    2. πŸ‘Ž 0
    posted by Damon
  2. NOW
    What if you had said $650 ?????

    The real question is in a normal distribution with mean = 637.52 and sigma = 31.15 what is the probability of over 650?
    how far above mean? (650 - 637.52) = 12.48
    how many sigmas above mean?
    12.48 / 31.15 = .401 sigmas from mean
    So from table, what is probability beyond .401 sigma above mean ?
    from normal distribution table F(.400) = .345

    1. πŸ‘ 0
    2. πŸ‘Ž 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    Suppose you have $28.00 in your bank account and you start saving $18.25 every week. Your friend has $161.00 in his bank account and is widthdrawing $15 every week. When will your account balances be the same ?

    asked by mary on February 10, 2010
  2. Statistics

    A bank wishes to estimate the mean balances owed by their MasterCard customers within $75. The population standard deviation is estimated to be $300. If a 98% confidence interval is used, how many cardholders should be sample.

    asked by Bryant on January 26, 2010
  3. economics

    The Australian dollar is currently very high, with a value of US$0.80. Many people expect the Australian dollar to rise even higher by the end of the year, to as much as US$0.90. Use a ‘°FOREX‘± (foreign exchange market)

    asked by Gary.L on June 7, 2007
  4. CHarter One Bank (Personal Finance)

    For Personal Finance I am suppose to answer some questions about the bank Charter One. I called my local bank and they are closed so I was wondering if any of you guys knew these answers? ATM's conveniently located? Fees? How

    asked by Sarah on September 15, 2010
  5. math

    Suppose $5000 is deposited in a bank account that compounds interest four times per year. The bank account contains $9900 after 13 years. What is the annual interest rate for this bank account? i already set it up but i don't know

    asked by Patty on April 10, 2012
  6. math

    Suppose $5000 is deposited in a bank account that compounds interest four times per year. The bank account contains $9900 after 13 years. What is the annual interest rate for this bank account? i already set it up but i don't know

    asked by Please help! on April 9, 2012
  7. math

    I have been staring at this problem forever, and cant seem to dig it up in my book. Please help! Two competing bank are trying to attract customers. (a) Ally Bank has an account which earns 25% interest every 10 years. Assuming

    asked by fawn on January 8, 2013
  8. calculus

    Suppose $5000 is deposited in a bank account that compounds interest four times per year. The bank account contains $9900 after 13 years. What is the annual interest rate for this bank account?

    asked by Zoey on April 9, 2012
  9. Algebra

    Use a calculator to find the mean and standard deviation of the data. Round to the nearest tenth. 6,7,19,7,18,7 A. mean = 9; standard deviation = 26.4 B. mean = 11.9; standard deviation = 26.4 C. mean = 10.6; standard deviation =

    asked by Veronika on February 18, 2016
  10. Statistics

    A college statistics class conducted a survey of how students spend their money. They asked 25 students to estimate how much money they typically spend each week on fast food. They determined that the mean amount spent on fast

    asked by sam on October 14, 2016

More Similar Questions