Final answer:
The probability P(z <= 8.78) in a standard normal distribution is approximately 1, as 8.78 is significantly greater than values typically listed in a z-table, and the area to the left of z = 8.78 accounts for almost the entire area under the curve.
Step-by-step explanation:
To calculate the probability P(z <= 8.78) in a standard normal distribution, you use a z-table, calculator, or computer algorithm. However, because 8.78 is much greater than any value found in a typical z-table, which usually do not go past 3 or 4, it's safe to assume that P(z <= 8.78) is virtually 1 (or 100%). This is because the area under the curve to the left of z = 8.78 encompasses almost the entire area under the standard normal curve.
Another way to find this probability is by using normalcdf function on a calculator, such as TI-83, 83+, or 84+ series, which for a large z-score like 8.78 would also give a result of approximately 1.