Assume that the random variable X is normally distributed, with mean $\mu$ = 60 and standard deviation $\sigma$ = 12. Compute the probability $\mathrm { P } ( \mathrm { X }

Question

Assume that the random variable X is normally distributed, with mean $\mu$ = 60 and standard deviation $\sigma$ = 12. Compute the probability $\mathrm { P } ( \mathrm { X } < 75 )$
A)0.8944
B)0.8849
C)0.1056
D)0.9015

Quizplus · Accepted Answer

To find $ P(X < 75) $ for a normally distributed variable X with mean $\mu = 60$ and standard deviation $\sigma = 12$, we first calculate the Z-score for X = 75 using the formula $Z = \frac{X - \mu}{\sigma}$. Substituting the given values, we get $Z = \frac{75 - 60}{12} = \frac{15}{12} = 1.25$. Looking up the Z-score of 1.25 in the standard normal distribution table gives a probability of approximately 0.8944, indicating that $P(X < 75) = 0.8944$.

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