A random variable X follows a normal distribution with mean 20. (standard deviation 5)
Find probability 14=

Question

A random variable X follows a normal distribution with mean 20. (standard deviation 5)
Find probability 14=<X=<26

anonymous · Answer

$$14 \le x \le 26$$

kropot72 · Answer

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

anonymous · Answer

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

kropot72 · Answer

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

anonymous · Answer

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?

kropot72 · Answer

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/

kropot72 · Answer

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

anonymous · Answer

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! :)

kropot72 · Answer

You're welcome :)