Question

Calcium levels in people are normally distributed with a mean of 9.5 mg/dL and a standard deviation of 0.3 mg/dL. Individuals with calcium levels in the bottom 10% of the population are considered to have low calcium levels. Find the calcium level that is the borderline between low calcium levels and those not considered low. Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

Answer 1

Answer:

9.1 mg/dL

Explanation:

A normal distribution is symmetrical, the area below the curve of negative Z-scores is equal to the area below the curve of positive Z-scores, Z measures the statistic observed and the parameter of the population.

And it is:

Z = (x - μ)/σ

where μ is the mean (9.5 mg/dL), x is the borderline, and σ is the standard deviation, which is 0.3 mg/dL.

The Z-score can be calculated in excel by the function =NORMSINV, and the factor will be the percente considered (10% = 0.1)

NORMSINV(0.1) = -1.28155

So,

-1.28155 = (x - 9.5)/0.3

x - 9.5 = -0.384465

x = 9.1 mg/dL