Suppose the distribution of serum-cholesterol values is normally distributed, wi

Question

Suppose the distribution of serum-cholesterol values is normally distributed, with mean = 200 + log(DGC) =......... mg/dL and standard deviation = 35 + log(DGC) = 37.48 mg/dL. (a) What is the probability that a serum-cholesterol will range between 220 + log(DGC) = ......... and 250 + 2log(DGC) = ...... inclusive (that is, high normal range)? Assume that cholesterol values can be measured exactly - that is, without the need for incorporating a continuity correction. (b) What is lowest quantile of serum-cholesterol values (the 20^th percentile)? (c) What is the highest quintile of serum-cholesterol values (the 80^th percentile)?

Explanation / Answer

(a) DGC = 305

Mean = 220 + log (DGC) = 220 + log (305) = 222.48 mg/ dL

Standard Deviation = 35 + log (DGC) = 35 + log ( 305) = 37.48 mg/ dL

Probability of range between 220 + log (DGC) = 222.48 mg/ dL and 250 + 2 log (DGC) = 254. 97 mg/dl

Pr( 222.48 <= cholestrol value < = 254.97 ; 222.48 ; 37.48)

Z- value = ( 254.97 - 222.48)/ 37.48 = 0.867

P - value = 0.5 - 0.193 = 0.307

(b) 20th percentile is let say X mg/ dL

Pr( x <=X ; 222.48; 37.48) = 0.2

Respective z - value = -0.842

so (X - 222.48)/ 37.48 = -0.842

X = -0.842 * 37.48 + 222.48 = 190.92mg/dL

(c) THe 80th percentile is let say Y mg/dL

Pr( x <=X ; 222.48; 37.48) = 0.8

Respective z - value = 0.842

so (X - 222.48)/ 37.48 = 0.842

X = 0.842 * 37.48 + 222.48 = 254.04 mg/ dL

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