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

Question

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

Quizplus · Accepted Answer

The probability $ \mathrm{P}(-a < z < a) = 0.4314 $ corresponds to the middle 43.14% of the standard normal distribution. This means that $a$ is the z-score that leaves 28.43% in each tail (since 100% - 43.14% = 56.86%, and 56.86%/2 = 28.43%). The z-score for 28.43% in the left tail is approximately 0.57.

Assume That zzz Scores Are Normally Distributed with a Mean of 0 and of 0

Assume That $z$ Scores Are Normally Distributed with a Mean of 0 and of 0