Final answer:
To find the 9th percentile, you can use the Z-score formula. The Z-score is calculated by subtracting the mean from the given value and then dividing by the standard deviation. For this question, the 9th percentile of the normally distributed random variable X is approximately 46.64.
Step-by-step explanation:
To find the 9th percentile, we can use the Z-score formula. The Z-score is calculated by subtracting the mean from the given value and then dividing by the standard deviation. For the 9th percentile, we need to find the Z-score that corresponds to a cumulative probability of 0.09. Using a standard normal distribution table or calculator, we find that the Z-score is approximately -1.34.
Next, we can use the Z-score formula to find the corresponding value at the 9th percentile.
Z = (X - μ) / σ
-1.34 = (X - 52) / 4
Solving for X:
-1.34 * 4 = X - 52
-5.36 = X - 52
X = 52 - 5.36
X ≈ 46.64
Therefore, the 9th percentile of the normally distributed random variable X is approximately 46.64.