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    A couple Normal Distribution Probability problems




    I've been trying to figure out the answer to these two problems for weeks, but I can't seem to figure out how to do them. Please let me know if you can help.

    1) A random variable X follows a normal distribution mean mu and standard dev 14. If P(X>148)=.96835 find mu

    2) A researcher is studying unemployment among insurance executives. He wishes to estimate mu, the average length of unemployment for this specific population. He plans to take a random sample of 36 recently employed insurance executives, and to estimate mu using the mean or the sample. Find the probability that the sampling error for his estimate is less than 1.26 weeks.

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    Re: A couple Normal Distribution Probability problems

    Can you write out the questions exactly as they were presented to you.
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    Re: A couple Normal Distribution Probability problems

    That is the way the problems were presented. That's part of the reason I'm a bit lost.

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    Re: A couple Normal Distribution Probability problems

    Look,in the first exercise I believe you just need to normalize the variable

    First you need to know, if X is N(\mu,\sigma^2) \rightarrow \frac{X-\mu}{\sigma} is N(0,1) standard normal.

    If X is N(\mu,14^2), so P(X>148)=0.96835 \rightarrow P(\frac{X-\mu}{\sigma}>\frac{148-\mu}{14})=0.96835\rightarrow P(Z>\frac{148-\mu}{14})=0.96835 where Z\rightarrow N(0,1)

    Now you just need to finish with the help of a standard normal table.
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    Re: A couple Normal Distribution Probability problems

    Quote Originally Posted by meaght12 View Post
    1) A random variable X follows a normal distribution mean mu and standard dev 14. If P(X>148)=.96835 find mu
    For a Standard Normal distribution, find Z with a cumulative probability of 1 - 0.96835. Next, calculate mu using Z = (X-mu)/s

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    meaght12 (12-11-2014)

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    Re: A couple Normal Distribution Probability problems

    I understand what you are saying, but I'm still a bit lost. We are told to be able to do this problem with the Norm.Dist or Norm.Inv function in excel so I'm not sure how to do it by hand.

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    Re: A couple Normal Distribution Probability problems

    Quote Originally Posted by meaght12 View Post
    I understand what you are saying, but I'm still a bit lost. We are told to be able to do this problem with the Norm.Dist or Norm.Inv function in excel so I'm not sure how to do it by hand.
    Look, I do not know how to do that excel, you use the R software?
    Anyway
    In R you just need to make qnorm(x) and then it will calculate the value of "a" such that P(X\leq a)=x.
    If P(Z>\frac{148-\mu}{14})=0.96835\rightarrow P(Z\leq \frac{148-\mu}{14})=1-0.96835\rightarrow P(Z\leq \frac{148-\mu}{14})=0.03165. Now using qnorm(0.03165)=-1.857078 we have
    \frac{148-\mu}{14}=-1.857078. Now just solve and find \mu
    Last edited by askazy; 12-11-2014 at 04:29 PM.
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    Re: A couple Normal Distribution Probability problems


    X = NORM.INV(probability, mean, standard deviation); for Standard Normal distribution mean = 0, s = 1.
    Z = NORM.INV(1-0.96865, 0, 1) = -1.86131

    Z = (X - mu)/s
    -1.86131 = (148 - mu)/14, solve for mu.

    See graph to visualize.
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