Final answer:
To determine Mrs. Collins's cholesterol level, we need to translate the percentage X into a z-score for a normal distribution and apply it to the known mean (μ) and standard deviation (σ). Since we don't have the exact value of X, we cannot provide a specific formula without additional information.
Step-by-step explanation:
To determine Mrs. Collins' cholesterol level in relation to the given percentile, we utilize the properties of a normal distribution. If the distribution of cholesterol levels among females aged Y and over is normally distributed with a known mean (μ) and standard deviation (σ), and Mrs. Collins's cholesterol level is higher than X% of this group, we can find her cholesterol level by using a z-score table or a standard normal distribution calculator. The z-score corresponding to X% will give us the number of standard deviations Mrs. Collins's cholesterol level is from the mean.
Without the specific value of X, we cannot definitively determine which option (A, B, C, or D) is correct. However, if we assume that X represents a probability below the mean, Mrs. Collins' cholesterol level would be a negative z-score, which equates to the mean minus some number of standard deviations (μ - zσ, where z is the z-score corresponding to X%). If X represents a probability above the mean, it would be a positive z-score, which equates to the mean plus some number of standard deviations (μ + zσ). Noteworthy examples of z-scores are 1.645 for the 95th percentile and 1.960 for the 97.5th percentile in a one-sided test.