If X is normally distributed with μ = 60 and σ = 5,find P(X 72).
A) 0.0082
B) 0.0123
C) 0.2731
D) 0.2968
E) 0.4918

Question

If X is normally distributed with μ = 60 and σ = 5,find P(X > 72).
A) 0.0082
B) 0.0123
C) 0.2731
D) 0.2968
E) 0.4918

Quizplus · Accepted Answer

To find $P(X > 72)$ for a normal distribution with $\mu = 60$ and $\sigma = 5$, we first calculate the Z-score: $Z = \frac{X - \mu}{\sigma} = \frac{72 - 60}{5} = 2.4$. Looking up 2.4 in the Z-table gives the area to the left of Z, so $P(Z < 2.4)$ is approximately 0.9918. Since we want $P(X > 72)$, we calculate $1 - P(Z < 2.4) = 1 - 0.9918 = 0.0082$.

If X Is Normally Distributed with μ = 60 and σ