Given a normal random variable x with mean of 82 and standard deviation of 12, the value of the standard normal random variable z associated with x = 70 is smaller than zero.

Question

Quizplus · Accepted Answer

To find the value of the standard normal random variable z associated with x = 70, we use the formula z = (x - μ)/σ, where μ is the mean and σ is the standard deviation. Plugging in the values given, we get:

z = (70 - 82)/12
z = -1

Since z represents the number of standard deviations away from the mean, a z value of -1 means that the value of x = 70 is one standard deviation below the mean. Since the standard normal distribution has a mean of 0 and standard deviation of 1, a z score of -1 corresponds to a value below the mean, and thus is smaller than zero. Therefore, the statement is true and the answer is A.

Given a Normal Random Variable X with Mean of 82