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  1. #1
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    stressed dad needs help!

    Hi, I am new to the forum and need help with a question from my daughter studying first year business, can anybody supply the answer below....thanks

    . The weekly salary paid to employees of a small company that supplies part-time laborers averages $700 with a standard deviation of $400.

    1) If the weekly salaries are normally distributed, estimate the fraction of employees that make more than $300 per week.

    2) If every employee receives a year-end bonus that adds $100 to the paycheck in the final week, how does this change the normal model for that week?

    3) If every employee receives a 5% salary increase for the next year, how does the normal model change?

    4) If the lowest salary is $300 and the median salary is $500, does a normal model appear appropriate?
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  2. #2
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    Re: stressed dad needs help!

    Question 1 requires the use of the 68, 95, 99.7 rule. Does your daughter know that?
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  3. #3
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    Re: stressed dad needs help!

    Quote Originally Posted by ericthered View Post
    Hi, I am new to the forum and need help with a question from my daughter studying first year business, can anybody supply the answer below....thanks

    . The weekly salary paid to employees of a small company that supplies part-time laborers averages $700 with a standard deviation of $400.

    1) If the weekly salaries are normally distributed, estimate the fraction of employees that make more than $300 per week.
    Do you or your daughter know what the "normal distribution" is? The "standard normal distribution" variable would be z= (x- 700)/400. Here, x= 300 so this is (300- 700)/400= -400/400= -1. So what is P(-1) in the standard normal distribution? There is no simple way to "calculate" that- you have to look it up in a table of the normal distribution. There is a good one at Standard Normal Distribution Table.

    2) If every employee receives a year-end bonus that adds $100 to the paycheck in the final week, how does this change the normal model for that week?
    Adding $100 one week clearly changes the mean- by how much? Do you think it would change the standard deviation?

    3) If every employee receives a 5% salary increase for the next year, how does the normal model change?
    Increasing the salary by 5% increases the mean by 5%.

    4) If the lowest salary is $300 and the median salary is $500, does a normal model appear appropriate?
    That clearly depends upon what YOU consider "appropriate"!
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    Re: stressed dad needs help!

    Thanks for help will look further into this!
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    Re: stressed dad needs help!

    Thanks for help will look further into this1
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    Re: stressed dad needs help!

    Quote Originally Posted by HallsofIvy View Post
    Increasing the salary by 5% increases the mean by 5%.
    True - and it also increases the standard deviation by 5%.
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    Re: stressed dad needs help!

    Quote Originally Posted by ebaines View Post
    True - and it also increases the standard deviation by 5%.
    Yes, thanks.
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    Re: stressed dad needs help!

    Quote Originally Posted by HallsofIvy View Post
    That clearly depends upon what YOU consider "appropriate"!
    Not entirely sure I get this response. If the data come from a Normal process than to observe half of all data points lying in an interval that is half a standard deviations width, would suggest that the distribution is HIGHLY right skewed and definitely non-Normal.
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