Discussion
The random variable X follows normal distribution with mean 5 and standard deviation 6. Hence :
Answer: D
The correct statement is \(P[X \ge 5] \gt P[X \ge 6]\).
The mean is 5, so \(P[X \ge 5] = 0.5\). Since 6 lies above the mean, \(P[X \ge 6] = P[Z \ge 1/6] \approx 0.43 \lt 0.5\). In general \(P[X \ge a]\) decreases as \(a\) increases.
The others are false: \(P[X \le 6] \approx 0.57\) is not equal to \(P[X \ge 5] = 0.5\) (A), \(P[X \le 5] = 0.5 \lt P[X \le 6]\) (B), and C reverses the true inequality.
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