Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If $P ( - a

Question

Assume that  z  scores are normally distributed with a mean of 0 and a standard deviation of  1. If $P ( - a < z < a )$  =0.4314 , find $a .$
A)  -0.18 
B)  0.3328 
C)  0.57 
D)  1.49

Quizplus · Accepted Answer

Given that $P(-a < z < a) = 0.4314$, this means we are looking for the value of $a$ such that the area under the standard normal curve (mean = 0, standard deviation = 1) between $-a$ and $a$ is 0.4314. The symmetry of the normal distribution around the mean (0) implies that half of 0.4314 (which is approximately 0.2157) lies to the right of the mean up to $a$, and the other half lies to the left of the mean down to $-a$. Looking up 0.2157 in the standard normal distribution table (or using a calculator that can compute inverse normal probabilities) gives a z-score close to 0.57, which corresponds to option C.

Assume That Z Scores Are Normally Distributed with a Mean