Calcium levels in people are normally distributed with a mean of 9.5 mg/dL and a standard deviation of 0.5 mg/dL. Individuals with calcium levels in the bottom 5% 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.

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ChiKesselman ChiKesselman · Answer 1 · 2020-03-17T06:08:02+01:00

Answer:

Individuals with calcium level 8.7 mg/dL or low are considered with low calcium level and above that are not considered low.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 9.5 mg/dL

Standard Deviation, σ = 0.5 mg/dL

We are given that the distribution of calcium levels is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.05

[tex]P( X < x) = P( z < \displaystyle\frac{x - 9.5}{0.5})=0.05[/tex]

Calculation the value from standard normal z table, we have,

[tex]\displaystyle\frac{x - 9.5}{0.5} = -1.645\\\\x =8.6775\\x \approx 8.7[/tex]

Thus, individuals with calcium level 8.7 mg/dL or low are considered with low calcium level and above that are not considered low.