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StatisticsQ&A Library4) Blood calcium levels are measured in mg/dL. In a group of patients over 30 you find the following: μ = 9.3 mg/dL, and σ = 2.35 mg/dL.a) Give the blood calcium values for the middle 50% of patients. (Hint/comment: if you want the middle 50%, how many percent go in each tail?)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.Question

Asked Sep 25, 2019

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4) Blood calcium levels are measured in mg/dL. In a group of patients over 30 you find the following: μ = 9.3 mg/dL, and σ = 2.35 mg/dL.

a) Give the blood calcium values for the middle 50% of patients. (Hint/comment: if you want the middle 50%, how many percent go in each tail?)

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.

Step 1

It is provided that the sample size, n is 30, mean is 9.3mg/dL and the standard deviation is 2.35 mg/dL.

Step 2

(a) The 50% in the middle leaves the other 25% in each tail, that is, 25^{th} and 75^{th} percentile. The z-value is obtained using Excel function =NORMSINV (percentile). Therefore, the corresponding z-values are obtained as ±0.6745 respectively.

Hence, the middle 50% of the patient’s blood calcium values is,

Step 3

(b) The 60% in the middle leaves the other 20% in each tail, that is, 20th and 80th percentile. The z-value is obtained using Excel function =NORMSINV (percentile). Therefo...

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