If $x$ is a normal random variable with $\mu=50$ and $\sigma=6$, then the probability that $x$ is not between 44 and 56 is
A) 0.6826 .
B) 0.3413 .
C) 0.8413 .
D) 0.3174 .

Question

Quizplus · Accepted Answer

The probability that $x$ is between 44 and 56 corresponds to $x$ being within one standard deviation ($\sigma=6$) of the mean ($\mu=50$). According to the empirical rule (or 68-95-99.7 rule) for normal distributions, approximately 68% of the data falls within one standard deviation of the mean. Therefore, the probability that $x$ is not between 44 and 56 is 1 - 0.68 = 0.32, which is closest to option D, 0.3174.

If xxx Is a Normal Random Variable With μ=50\mu=50μ=50 And σ=6\sigma=6σ=6 , Then the Probability That

If $x$ Is a Normal Random Variable With $\mu=50$ And $\sigma=6$ , Then the Probability That