Discussion
If X is a normal variate with mean 20 and variance 64, then P(X \(\gt\) 20) = ........................ .
Answer: C
P(X > 20) = 0.5.
A normal distribution is symmetric about its mean, which is also its median. With mean 20, exactly half the probability lies above 20 and half below, whatever the variance:
\[ P(X \gt 20) = P(Z \gt 0) = 0.5 \]
The variance of 64 (standard deviation 8) only affects how spread the distribution is. 20/64 wrongly mixes the mean with the variance; 0 and 1 would mean no values or all values lie above the mean.
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