Question

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P ( 0 < z < a ) = 0.4545 , find a.

a =

**Please show what you're putting in the calculator for example if you have to use the function normalcdf or invNorm if possible... if not please write it out fully thank you :-)

Answer 1

Z ~ N(0,1)

P(0 < Z < a) = 0.4545 i.e. (a) - (0) = 0.4545 i.e. (a) - 0.5 = 0.4545 i.e. (a) = 0.4545 + 0.5 = 0.9545

[(.) is the cdf of N(0,1)]

In order to obtain the cdf of 0, we have to put 0 is the cdf option of normal distribution calculator.

Thus, a = (0.9545)

In order to obtain inverse cdf of 0.9545, we have to put 0.9545 in the inverse cdf option of normal distribution calculator.

Hence, a = 1.69 (Ans).