Answer: To find the probability that a normally distributed random variable X with mean 79 and standard deviation 7 is less than 65, we need to standardize the value 65 using the z-score formula:
z = (x - mu) / sigma
where x is the value we want to standardize, mu is the mean, and sigma is the standard deviation.
Plugging in the values we get:
z = (65 - 79) / 7
z = -14 / 7
z = -2
Using a standard normal distribution table, we can find that the probability of a standard normal random variable being less than -2 is approximately 0.0228.
Therefore, P(X < 65) = P(Z < -2) ≈ 0.0228.
The answer is not one of the given options, but it is closest to option B (0.025), which represents the probability of a standard normal random variable being less than -1.96.
Explanation: