Question

ch 3 what percentage of values of a variable following the standard normal distribution is between z - scores of 0 and 3?
94.5%
90.7%
49.5%
33.2%

Explanation:

Step1: Recall standard - normal table

The standard - normal distribution has a mean of 0 and a standard deviation of 1. The cumulative distribution function $\varPhi(z)$ gives the probability that a standard - normal random variable $Z$ is less than or equal to $z$, i.e., $P(Z\leq z)=\varPhi(z)$.

Step2: Calculate $P(0 < Z < 3)$

We know that $P(0 < Z < 3)=P(Z < 3)-P(Z < 0)$. From the standard - normal table, $P(Z < 3)\approx0.9987$ and $P(Z < 0) = 0.5$. Then $P(0 < Z < 3)=0.9987 - 0.5=0.4987\approx49.5\%$.

Answer:

C. 49.5%