The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. **Please show written work! It is difficult to understand "text" work/answers with mathematical/statistical problems** 1. For what value of z does exactly 95% of the area under a Gaussian curve lie between ± z? Use this multiplier to find the range of measured cholesterol concentrations that would include 95% of the trials from the “parent population” (μ and σ) given above. 2. Calculate z for a trial in which the measured total cholesterol concentration is 6.302 mmol/L. 3. What is the probability that a trial will give a cholesterol concentration below 6.302 mmol/L? What is the (complementary) probability that a trial will give a cholesterol concentration above 6.302 mmol/L? Again, sketch these areas.
The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. **Please show written work! It is difficult to understand "text" work/answers with mathematical/statistical problems**
1. For what value of z does exactly 95% of the area under a Gaussian curve lie between ± z? Use this multiplier to find the
2. Calculate z for a trial in which the measured total cholesterol concentration is 6.302 mmol/L.
3. What is the probability that a trial will give a cholesterol concentration below 6.302 mmol/L? What is the (complementary) probability that a trial will give a cholesterol concentration above 6.302 mmol/L? Again, sketch these areas.
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