# Thread: A couple Normal Distribution Probability problems

1. ## 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.

2. ## Re: A couple Normal Distribution Probability problems

Can you write out the questions exactly as they were presented to you.

3. ## 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.

4. ## 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 is N(0,1) standard normal.

If X is , so where

Now you just need to finish with the help of a standard normal table.

5. ## Re: A couple Normal Distribution Probability problems

Originally Posted by meaght12
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

6. ## The Following User Says Thank You to Miner For This Useful Post:

meaght12 (12-11-2014)

7. ## 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.

8. ## Re: A couple Normal Distribution Probability problems

Originally Posted by meaght12
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 .
If . Now using we have
. Now just solve and find

9. ## 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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