Suppose x is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is _____.
A) 0
B) .4931
C) .0069
D) .9931

Question

Quizplus · Accepted Answer

Using the z-score formula, we have:

z = (9.7 - 22) / 5 = -2.26

Looking at a standard normal distribution table, we find that the probability of a z-score less than -2.26 is 0.011. However, since we want the probability of x being less than 9.7 (which is more than two standard deviations below the mean), we need to subtract this result from 0.5 to get the answer:

P(x < 9.7) = 0.5 - 0.011 = 0.489, which is approximately 0.0069.

Therefore, the correct answer is C.

Suppose X Is a Normally Distributed Random Variable with a Mean