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.

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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.

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Expert Answer

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, 25th and 75th 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,

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Middle 50% values = u± xo 9.3+0.6745(2.35) =(7.71,10.88)

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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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Middle 60% values ux -9.3+ 0.8416(2.35) - ( 7.32,11.28)

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