A normal random variable X has mean 40 and standard deviation 16. Find the area under the normal curve above the interval 16-60.
A) 0.8089
B) 0.8276
C) 0.8962
D) 0.7324

Question

Quizplus · Accepted Answer

To find the area under the normal curve between 16 and 60 for a normal distribution with mean 40 and standard deviation 16, we first convert these values to Z-scores. For 16: Z = (16 - 40) / 16 = -1.5. For 60: Z = (60 - 40) / 16 = 1.25. Using standard normal distribution tables or a calculator, we find the area to the left of Z = 1.25 and subtract the area to the left of Z = -1.5. The area to the left of Z = 1.25 is approximately 0.8944, and the area to the left of Z = -1.5 is approximately 0.0668. Subtracting these gives 0.8944 - 0.0668 = 0.8276.

A Normal Random Variable X Has Mean 40 and Standard