Question

Blood calcium levels are measured in mg/dL. In a group of patients over 30 you find the following: μ = 8.9 mg/dL, and σ = 2.40 mg/dL. a) Give the blood calcium values for the middle 50% of patients.

b) Give the blood calcium values for the middle 60% of patients.

c) Give the 80th percentile.

d) Are you surprised by the answers to (b) and (c)? Explain. If you're not sure what's going on, draw some pictures of the normal curves.

Answer 1

Solution:-

μ = 8.9 mg/dL, and σ = 2.40 mg/dL.

a) The blood calcium values for the middle 50% of patients.is 7.28 and 10.52.

p-value for the middle 50% = 0.25 and 0.75

z-score for the p-value = + 0.675

By applying normal distribution:-

x₁ = 7.28

x₂ = 10.52

b) The blood calcium values for the middle 60% of patients is 6.879 and 10.921.

p-value for the middle 60% = 0.20 and 0.80

z-score for the p-value = + 0.842

By applying normal distribution:-

x₁ = 6.879

x₂ = 10.921

c) The 80th percentile is 10.921

p-value for the bottom 80% = 0.80

z-score for the p-value = - 0.842

By applying normal distribution:-

x = 10.921

d) Yes, we are surprised, the 80th percentile and the one of the boundary of the middle 60% of the patients are same.