Final answer:
The percentage of students who scored one standard deviation above the mean on an exam with a mean of 150 and a standard deviation of 30 is approximately 84%. This is derived from the empirical rule or 68-95-99.7 rule, which states that about 68% of the data in a normal distribution is within one standard deviation of the mean; hence, half of this percentage is above the mean (34%) and when added to the 50% (mean), it yields 84%.
Step-by-step explanation:
If the mean of an exam was 150 with a standard deviation of 30, we need to determine what percentage of students scored one standard deviation above the mean. In a normal distribution, which is often assumed for test scores, the percentages of data within certain standard deviations from the mean are fixed. Specifically, about 68% of data lies within one standard deviation of the mean (either above or below), 95% within two standard deviations, and 99.7% within three standard deviations.
So, to find the percentage of students who scored one standard deviation above the mean, we look at what is known as the empirical rule or the 68-95-99.7 rule. To answer the question, we consider that half of the 68% lies above the mean and half lies below. This means that 34% of students scored above one standard deviation of the mean, and 34% scored below one standard deviation of the mean.
Therefore, if we want the percentage of students who scored specifically above the mean by one standard deviation, we must add 34% (the percentage above the mean within one standard deviation) to the 50% (the percentage up to the mean) to get approximately 84%. So, the correct answer is B. 84% of students scored one standard deviation above the mean.