Final answer:
To find the value of z that satisfies the equation P(Z < z) = 0.9115, we need to use the inverse normal distribution. The z-score that corresponds to an area of 0.9115 is approximately 1.28.
Step-by-step explanation:
To find the value of z that satisfies the equation P(Z < z) = 0.9115, we need to use the inverse normal distribution. The given equation represents the area to the left of z. To find the z-score that corresponds to an area of 0.9115, we can use a z-table or a calculator with a normal distribution function. Looking up the value in the table or using the calculator, we find that z = 1.28 (approximately).