standard normal variable- 2007 FRM

[mastvikas]

Please Help me in understanding the below sum-:

Let Z be a standard normal random variable and N(z) the cumulative distribution function. An event X is defined to happen if either z takes a value between +1 and -1or z takes any value greater than 1.5. What is the probability of event X happening if N(1) = 0.8413, N(1/2) = 0.6915 and N(-1.5) = 0.0668, where N(•) is the cumulative distribution function of a standard normal variable?

a. 0.083
b. 0.2166
c. 0.6826
d. 0.7494

 

[Aleksander Hansen]

Area between -1 and +1 = 68.26% (since N(0)= 0.5, we have 0.8413-0.5 = 0.3413. 0.3413x2 = 68.26% due to the symmetry of the Normal distribution. Simply add the area below -1.5 to get the answer. That is 68.26% + 6.68% = 74.94%, or 0.7494. The answer is d).

 

[mastvikas]

Thanks Alekxsander