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 standard normal distribution is symmetric about its mean, 0. Reflecting values at or above z across 0 gives values at or below −z. Therefore, the two probabilities are equal, so the probability of being less than or equal to −z standard deviations from the mean is p%.

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