Find the specified percentile, quartile, or decile.
-The serum cholesterol levels for men in one age group are normally distributed with a mean of 178.2 and a standard deviation of 40.8. All units are in mg/100 mL. Find the 9th percentile.
A)161.5 mg/100mL
B)123.5 mg/100mL
C)107.2 mg/100mL
D)165.1 mg/100mL

Question

Find the specified percentile, quartile, or decile.
-The serum cholesterol levels for men in one age group are normally distributed with a mean of 178.2 and a standard deviation of 40.8. All units are in mg/100 mL. Find the 9th percentile. 
A)161.5 mg/100mL
B)123.5 mg/100mL
C)107.2 mg/100mL
D)165.1 mg/100mL

Quizplus · Accepted Answer

To find the 9th percentile of a normally distributed set of data, we use the formula for the z-score in relation to percentiles. The 9th percentile corresponds to a z-score that we can find using a z-table or a calculator designed for statistics. The formula to convert a z-score to the actual value in the context of a normal distribution is X = μ + Zσ, where X is the value we're looking for, μ is the mean, Z is the z-score corresponding to the 9th percentile, and σ is the standard deviation.For the 9th percentile, the z-score is approximately -1.34 (this value can be found in z-tables or statistical calculators). Using the given mean (μ = 178.2) and standard deviation (σ = 40.8), we can calculate the 9th percentile as follows:X = μ + Zσ = 178.2 + (-1.34)(40.8) ≈ 178.2 - 54.7 ≈ 123.5 mg/100 mL.Therefore, the 9th percentile of the serum cholesterol levels is approximately 123.5 mg/100 mL.

Find the Specified Percentile, Quartile, or Decile