Assume that the random variable X is normally distributed, with mean $\mu$ = 60 and standard deviation $\sigma$ = 8. Compute the probability $\mathrm { P } ( 38

Question

Assume that the random variable X is normally distributed, with mean $\mu$ = 60 and standard deviation $\sigma$ = 8. Compute the probability $\mathrm { P } ( 38 < \mathrm { X } < 70 )$
A)0.8914
B)0.8819
C)0.8944
D)0.7888

Quizplus · Accepted Answer

To find $P(38 < X < 70)$, we convert the values to Z-scores: $Z = \frac{X - \mu}{\sigma}$. For X = 38, $Z = \frac{38 - 60}{8} = -2.75$, and for X = 70, $Z = \frac{70 - 60}{8} = 1.25$. Using a standard normal distribution table or calculator, we find $P(-2.75 < Z < 1.25)$ = 0.8914.

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