Final answer:
To find P(y ≤ 8) for a normal distribution with mean 4 and standard deviation 9, we calculate the z-score for 8 and find the corresponding probability using the z-score table.
Step-by-step explanation:
To find P(y ≤ 8), we need to calculate the standard z-score for 8 using the formula:
z = (x - mean) / standard deviation
where x is the value we want to find the probability for, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.
Using the given information that y is distributed N(4,9), we plug in the values:
z = (8 - 4) / √9 = 2 / 3 = 0.6667
Now, using the z-score table, we find the corresponding probability for z = 0.6667, which is approximately 0.7486. However, since we need to find P(y ≤ 8), we need to include the area to the left of the z-score, which is 0.7486 + 0.5 = 0.8746.
Therefore, P(y ≤ 8) is approximately 0.8746.