If we know that the probability for z 1.5 is .067, then we can say that
A) the probability of exceeding the mean by more than 1.5 standard deviations is .067.
B) the probability of being more than 1.5 standard deviations away from the mean is .134.
C) 86.6% of the scores are less than 1.5 standard deviations from the mean.
D) all of the above

Question

If we know that the probability for z > 1.5 is .067, then we can say that
A) the probability of exceeding the mean by more than 1.5 standard deviations is .067.
B) the probability of being more than 1.5 standard deviations away from the mean is .134.
C) 86.6% of the scores are less than 1.5 standard deviations from the mean.
D) all of the above

Quizplus · Accepted Answer

A) This statement is correct because a z-score of 1.5 indicates a value that is 1.5 standard deviations above the mean, and the given probability of .067 matches this scenario. B) Since the normal distribution is symmetric, the probability of being more than 1.5 standard deviations away from the mean includes both tails (above and below), doubling the one-tail probability to .134. C) Since the probability of being more than 1.5 standard deviations away from the mean is .134 (from B), the proportion within 1.5 standard deviations from the mean is 1 - .134 = .866 or 86.6%.

If We Know That the Probability for Z > 1