If X is normally distributed with μ = 150 and σ = 30,find P(90

Question

If X is normally distributed with μ = 150 and σ = 30,find P(90 < X < 180).
A) 0.1359
B) 0.8185
C) 0.3185
D) 0.8243
E) 0.8173

Quizplus · Accepted Answer

To find $P(90 < X < 180)$ for a normal distribution with $\mu = 150$ and $\sigma = 30$, we standardize the values and use the Z-table. Standardizing gives $Z = \frac{X - \mu}{\sigma}$. For $X = 90$, $Z = \frac{90 - 150}{30} = -2$, and for $X = 180$, $Z = \frac{180 - 150}{30} = 1$. Looking up these Z-values in the standard normal distribution table, we find $P(Z < -2) \approx 0.0228$ and $P(Z < 1) \approx 0.8413$. The probability that $X$ is between 90 and 180 is $P(Z < 1) - P(Z < -2) = 0.8413 - 0.0228 = 0.8185$.

If X Is Normally Distributed with μ = 150 and σ