Final answer:
The correct answer is 'b. False' because probabilities range from 0 to 1 and cannot be negative. The probability of a z-score being less than or equal to 0 in a standard normal distribution is actually 0.5, and not -0.5, because probabilities cannot have negative values.
Step-by-step explanation:
The question 'The Prob. (Z ≤ 0) is -0.5' is asking whether the probability of a z-score being less than or equal to 0 can be negative, specifically -0.5. The correct answer is b. False.
In a normal distribution, the probability is represented by the area under the curve to the left of the z-score. Since the total area under the curve represents the whole probability space (which equals 1), a single tail probability can range from 0 to 1, but it can never be negative. Therefore, the probability that Z is less than or equal to 0 (which is the tail to the left of the mean in a standard normal distribution) is always a non-negative value. Specifically, in a standard normal distribution, the probability that Z is less than or equal to 0 is actually 0.5, because the distribution is symmetric around the mean (which corresponds to a z-score of 0).
It is important to note that the value of -0.5 does not make sense in the context of probabilities, as probabilities cannot be negative. Probabilities range from 0 to 1, where 0 indicates an impossible event, and 1 indicates a certain event. Hence, an answer of -0.5 does not align with the basic principles of probability and the properties of the standard normal distribution.