Assume that the random variable X is normally distributed, with mean $\mu$ = 80 and standard deviation $\sigma$ = 15. Compute the probability $\mathrm { P } ( X 92 )$
A)0.2119
B)0.1977
C)0.7881
D)0.2420

Question

Assume that the random variable X is normally distributed, with mean $\mu$ = 80 and standard deviation $\sigma$ = 15. Compute the probability $\mathrm { P } ( X > 92 )$
A)0.2119
B)0.1977
C)0.7881
D)0.2420

Quizplus · Accepted Answer

To find $P(X > 92)$ for a normally distributed variable with mean $\mu = 80$ and standard deviation $\sigma = 15$, we first calculate the Z-score for $X = 92$: $Z = \frac{92 - 80}{15} = \frac{12}{15} = 0.8$. Looking up the Z-score of 0.8 in a standard normal distribution table or using a calculator, we find that the area to the left of $Z = 0.8$ is approximately 0.7881. Since we want $P(X > 92)$, we subtract this from 1 to get $1 - 0.7881 = 0.2119$.

Assume That the Random Variable X Is Normally Distributed, with Mean