Final answer:
To find the 85th percentile of a normal population, use the z-score formula to find the corresponding value. In this case, the 85th percentile is approximately 58.25.
Step-by-step explanation:
To find the 85th percentile of a normal population with a mean of 51 and a standard deviation of 7, we can use the standard normal distribution. First, we need to find the z-score corresponding to the 85th percentile. The z-score can be found using the standard normal distribution table or a calculator. In this case, the z-score for the 85th percentile is approximately 1.036.
Next, we can use the formula z = (x - u) / s, where x is the value we want to find, u is the mean, and s is the standard deviation. Rearranging the formula, we have x = z * s + u. Plugging in the values, we get x = 1.036 * 7 + 51, which gives us approximately 58.25.
Therefore, the 85th percentile of the population is approximately 58.25.