Suppose that the creatine kinase levels among healthy males are normally distributed with a standard deviation of 23 units/L.

Question

Suppose that the creatine kinase levels among healthy males are normally distributed with a standard deviation of 23 units/L. Research shows that exactly 5% of the healthy males have a creatine kinase level above 151 units/L. What is the mean creatine kinase level in healthy males? Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Answer 1

Also applying the z-score formula for the standard normal distribution:

z = (X - μ) / σ

where:

X = Mean creatine kinase level in healthy males

μ = Mean of creatine kinase levels for healthy males

σ = Standard deviation of creatine kinase levels for healthy males = 23 units/L

We are given that precisely 5% of healthy males have a creatine kinase level above 151 units/L. This means the z-score corresponding to the 95th percentile is 1.645 (approximately). (Note that the z-score is positive because we are looking for the value above the mean.)

Now, we can rearrange the z-score formula to solve for the mean creatine kinase level (μ):

μ = X - z * σ

μ = 151 - 1.645 * 23

μ ≈ 151 - 37.835

μ ≈ 113.165

Healthy males' mean creatine kinase level is approximately 113.2 units/L.