If X has a normal distribution with µ = 100 and σ = 5, then the probability P(90 ≤ X ≤ 95) can be expressed in terms of a standard normal variable Z as ________.
A) P(2 ≤ Z ≤ 1)
B) P(-2 ≤ Z ≤ 1)
C) P(-2 ≤ Z ≤ -1)
D) P(-2 ≤ Z ≤ -2)

Question

Quizplus · Accepted Answer

To express the probability in terms of a standard normal variable Z, we use the transformation $Z = \frac{X - \mu}{\sigma}$. For $X = 90$, $Z = \frac{90 - 100}{5} = -2$, and for $X = 95$, $Z = \frac{95 - 100}{5} = -1$. Therefore, the probability $P(90 \leq X \leq 95)$ is equivalent to $P(-2 \leq Z \leq -1)$.

If X Has a Normal Distribution with µ = 100