1. ## normally distributed

If X is normally distributed with mean 40 and standard deviation of 0.8 , find the value of a such that

(1) P ( | X-40 | < a ) = 0.7521

(2) P ( | X-40 ) > a ) = 0.2812

Can someone pls show me the steps and what does it mean when modulus is applied to the variable X ?

If X is normally distributed with mean 40 and standard deviation of 0.8 , find the value of a such that

(1) P ( | X-40 | < a ) = 0.7521

(2) P ( | X-40 ) > a ) = 0.2812

Can someone pls show me the steps and what does it mean when modulus is applied to the variable X ?
(1) $\displaystyle \Pr( |X - 40| < a) = \Pr(-a < X - 40 < a)$ $\displaystyle = \Pr(-a + 40 < X < a + 40) = 1 - 2 \Pr(X < a + 40)$ by symmetry.

Therefore $\displaystyle \Pr(X < a + 40) = \frac{1 - 0.7521}{2} = ....$.

This has the form Pr( X < x*) = number, which is a type of question you should know how to do.

(2) $\displaystyle \Pr( |X - 40| > a) = \Pr(X - 40 > a) + \Pr(X - 40 < -a)$ $\displaystyle = 2 \Pr(X - 40 < -a) = 2 \Pr(X < -a + 40)$ by symmetry.

Therefore $\displaystyle \Pr(X < -a + 40) = \frac{0.2812}{2} = ....$ which is again a type of question you should know how to do.

3. ## Re :

thank u very much mr fantastic for clearing my doubts .