## nickersia Group Title A random variable X follows a normal distribution with mean 20. (standard deviation 5) Find probability 14=<X=<26 one year ago one year ago

1. nickersia Group Title

$14 \le x \le 26$

2. kropot72 Group Title

Do you know how to work out the z-scores for 14 and 26? $z=\frac{X-\mu}{\sigma}$

3. nickersia Group Title

Yes, but I'm not sure should I put 6 and -6 for z? That way I got 50 for x, which makes me no sense

4. kropot72 Group Title

$z _{1}=\frac{14-20}{5}=?$ $z _{2}=\frac{26-20}{5}=?$

5. nickersia Group Title

I got 76.98% as an answer. z= -1.2 and 1.2 So, z score from beginning of the curve to the s.d. of 1.2 is 0.8849, which meas that on the right it's 0.1151 and same on the left, so it's 0.2302. 23.02% are lower than 14 and bigger that 26, so 76.98% is X. Am I right?

6. kropot72 Group Title

A standard normal distribution table gives the following values for cumulative probability: z = 1.2 : p = 0.8849 z = -1.2 : p = 0.1151 You can check these results on the table at the following link (choose 'normal.pdf' from the menu: http://www.math.bgu.ac.il/~ngur/Teaching/probability/

7. kropot72 Group Title

$P(14<X <26)=0.8849-0.1151=?$

8. nickersia Group Title

0.7698 which is 76.98% So, I suppose I got it right :) That's basically the same thing I did, thank you very much! :)

9. kropot72 Group Title

You're welcome :)