Final answer:
To determine the 95th percentile score on a normally distributed test with a mean of 70 and a standard deviation of 8, we use a normal distribution calculator function, find the corresponding z-score, and apply it to the formula involving the mean and standard deviation.
Step-by-step explanation:
To find the score needed to be in the 95th percentile of a normally distributed test with a mean of 70 and a standard deviation of 8, we utilize the z-score table or a calculator function for normal distribution (such as invNorm on a TI calculator). The 95th percentile corresponds to the point on the distribution where 95% of the values lie below it.
We first find the z-score that corresponds to the 95th percentile. Using the invNorm function, we input the percentile as a decimal (0.95), the mean (70), and the standard deviation (8) to find the corresponding z-score. The formula to then calculate the actual test score is:
actual score = mean + (z-score * standard deviation).
After finding the z-score, we plug it into the formula to find the actual score. If we calculate it correctly, the closest answer from the provided options that would represent the 95th percentile score will be obtained.