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.

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

lhmarianateixeira lhmarianateixeira · Answer 2 · 2022-03-10T12:00:21+01:00

In this exercise, we have to use our knowledge of distribution and statistics to calculate the value of calcium, so we find that:

9.1 mg/dL is the low level of calcium.

What is a symmetric distribution?

In a symmetric distribution, the measures of central tendency coincide, that is, the mean, the mode and the median. If the distribution is left skewed or negative, the mean is less than the mode; being right skewed or positive, the mean is greater than the mode.

In this case we have a normal and symmetrical distribution so that the formula corresponding to this type of function is:

[tex]Z = (x - \mu)/\sigma[/tex]

where,

μ is the mean (9.5 mg/dL)
x is the borderline that we need to find
σ is the standard deviation (0.3 mg/dL.)

Knowing that mean is a constant that we will use this value, we can write it as:

[tex]-1.28155 = (x - 9.5)/0.3\\x - 9.5 = -0.384465\\x = 9.1 mg/dL[/tex]

See more about distribuition at brainly.com/question/10951564