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 that 43.14% of the data within a normal distribution (with a mean of 0 and standard deviation of 1) lies between $-a$ and $a$. The symmetry of the normal distribution implies that this percentage is centered around the mean. The value of $a$ that corresponds to this percentage can be found using standard normal distribution tables or a calculator designed for statistical analysis. The correct value of $a$ that approximates to the given probability is 0.57, which is option C.

Assume That Z Scores Are Normally Distributed with a Mean