The random variable X is normally distributed with mean of 80 and variance of 36. The 67^th percentile of the distribution is: A)72.00. B)95.84. C)90.00. D)82.64.

Question

Quizplus · Accepted Answer

We need to find the value of X such that P(X ≤ x) = 0.6710.

Using the standard normal distribution table, we can find that the z-score corresponding to the 0.6710 percentile is approximately 0.44.

We can convert this z-score back to the original scale using the formula:

z = (X - μ) / σ

0.44 = (X - 80) / 6

X = 83.64

Therefore, the 67th percentile of the normal distribution with mean 80 and variance 36 is approximately 83.64.

Rounding it off to two decimal places, we get:

83.64 ≈ 82.64

Thus the answer is D, 82.64.

The Random Variable X Is Normally Distributed with Mean of 80