Question

the probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. what can be said with certainty about the probability that the random variable is less than or equal to -z standard deviations from the mean?
the probability is less than p%
the probability is equal to p%
the probability is greater than p%
the probability is not equal to p%

Explanation:

Step1: Recall property of normal distribution

A standard - normal distribution is symmetric about the mean. The probability of a random variable being greater than or equal to \(z\) standard deviations from the mean is the same as the probability of it being less than or equal to \(-z\) standard deviations from the mean due to this symmetry.

Answer:

The probability is equal to \(p\%\)