Complete Question
The complete question is shown on the first uploaded image
Answer:
The calcium level that is the borderline between low calcium levels and those not considered low is [tex]c = 8.68[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 9.5\ mg/dL[/tex]
The standard deviation [tex]\sigma = 0.5 \ mg/dL[/tex]
The proportion of the population with low calcium level is [tex]p =[/tex]5% = 0.05
Let X be a X random calcium level
Now the P(X < c) = 0.05
Here P denotes probability
c is population with calcium level at the borderline
Since the calcium level is normally distributed the z-value is evaluated as
[tex]P(Z < \frac{c - \mu}{\sigma } ) = 0.05[/tex]
The critical value for 0.05 from the standard normal distribution table is
[tex]t_{0.05} = -1.645[/tex]
=> [tex]\frac{c - \mu}{\sigma } = -1.645[/tex]
substituting values
[tex]\frac{c - 9.5}{0.5 } = -1.645[/tex]
=> [tex]c - 9.5 = -0.8225[/tex]
=> [tex]c = 8.68[/tex]
