Final answer:
To find the z-score for P(Z > ?) = 0.4771, convert this to the area to the left, which is 0.5229, and look up this value in a z-table or use a calculator to find the corresponding z-score, which is 0.06.
Step-by-step explanation:
To find the z-score corresponding to a probability of P(Z > ?) = 0.4771, we first need to understand that the total area under the standard normal distribution curve is 1. Since most z-tables show the area to the left of the z-score, it means we need to find the area to the left which is 1 - 0.4771 = 0.5229. By looking up this area in a z-table or using a statistical calculator, we find the z-score that has an area of 0.5229 to its left. This z-score is 0.06.
It's important to note that the z-score reflects the number of standard deviations a value is from the mean in a standard normal distribution, which has a mean of 0 and a standard deviation of 1. To calculate the z-score, we can use the formula z = (x - µ) / σ, where x is the value, µ is the mean, and σ is the standard deviation of the original distribution.