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

Question

Quizplus · Accepted Answer

We know that the mean (μ) of the normal distribution is 80 and the variance (σ^2) is 36.
Hence, the standard deviation (σ) is the square root of variance i.e. σ = sqrt(36) = 6.

Now, to find the 67th percentile of the distribution, we need to find the z-score corresponding to it.

Using the standard normal distribution table, we can find that the z-score corresponding to the 67th percentile is approximately 0.44.

Therefore,

z = (X - μ) / σ
0.44 = (X - 80)/6
X = 80 + 0.44*6
X = 82.64 (rounded to two decimal places)

Hence, the 67th percentile of the distribution is 82.64.

Therefore, the best choice is (D).

The Random Variable X Is Normally Distributed with Mean of 80