Final answer:
The probabilities mentioned can be found using the Z-Table of the Standard Normal Distribution. The correct probabilities are A) p = 0.5641, B) p = 0.4893, and C) p = 0.6184.
Step-by-step explanation:
A normal distribution with a mean and a standard deviation of (a) refers to a standard normal distribution, which has a mean of 0 and a standard deviation of 1. In this case, the probabilities mentioned can be found using the Z-Table of the Standard Normal Distribution.
A) p = -0.50: This means finding the probability of randomly selecting a score less than -0.50. You can look up the value -0.50 in the Z-Table and find that the corresponding probability is 0.3085. Therefore, the correct answer is D) p = 0.3085.
B) p = 0.1587: This means finding the probability of randomly selecting a score less than 0.1587. Looking up the value 0.1587 in the Z-Table, you will find the corresponding probability to be 0.5641. Therefore, the correct probability is A) p = 0.5641.
C) p = 0.0228: This means finding the probability of randomly selecting a score less than 0.0228. Looking up the value 0.0228 in the Z-Table, you will find the corresponding probability to be 0.4893. Therefore, the correct probability is B) p = 0.4893.
D) p = 0.3085: This means finding the probability of randomly selecting a score less than 0.3085. Looking up the value 0.3085 in the Z-Table, you will find the corresponding probability to be 0.6184. Therefore, the correct probability is C) p = 0.6184.