# Probability with unknown sample mean and unknown standard deviation

I am studying statistics in a textbook. I have successfully answers two questions about normal distribution. Here are the questions

1. Credit scores are three-digit numbers used by lenders when evaluating your credit worthiness

A. Construct a histogram of the credit scores. Do the credit scores appear approximately normally distributed? Explain.

B.Construct a normal probability plot (QQ-plot) of the credit scores. Do the credit scores appear approximately normally distributed? Explain.

C. If your answer in (b) is yes, find the probability that a city will have a credit score of at least 680. Use the sample mean of the data for (miu) , and the sample standard deviation for (s). Here is the data for the questions :

670 705 680 690 653 675 675 655 667 672 707 688 671 688 660 676 686 691 675 693

For questions 1A , i plot a histogram in R and test the normality using Minitab and the statistics test shows that data is normally distributed . 1B also normally distributed. I want to ask how to work on 1C. My work goes this way

P(x>680) =..

SD = (X - Mean) / z

SD=(680-Mean)/1.96

Does my answer from 1a and 1b correct? Because im not sure graphically i found some data out of the straight line. And how can i do 1C for this? im stuck from SD and the Mean

You can calculate the sample mean and standard deviation from the data given. Then, you want $P(X>680)$. Calculate $z=\frac{X-\mu}{s}=m$(say). Then $P(X>680)=P(z>m)=1-P(z<m)$. Check the z-table for $z=m$. The value will give you $P(z<m)$.
• I don't think the standard deviation is correct. Use $s^2=\frac{1}{N-1}\sum(x_i-\bar x)^2$ – Tejas Nov 21 '15 at 8:32