Chapter 7 - Review - Case Study - A Tale of Blood Chemistry and Health - Page 398: 2

Section 1 To obtain the blood components that should be cause for concern for Abby, calculate z-score first: \[\begin{align} & z=\frac{\text{data value}-\text{average}}{\text{standard deviation}} \\ & =\frac{5.30-7.25}{1.625} \\ & =-1.2 \end{align}\] Now, go to Table V from the appendix to obtain the associated probability. Since the needed area is to the left, that is, $P(z-0.73)=1-P(z-0.46)=1-P( z<1.20)=1-0.8849=0.1151$ Hence, the probability for potassium serum result 5.1 is 0.1151. Section 9 To obtain the blood components that should be cause for concern for Abby, calculate z-score first: \[\begin{align} & z=\frac{\text{data value}-\text{average}}{\text{standard deviation}} \\ & =\frac{100.0-102.5}{3.25} \\ & =-0.77 \end{align}\] Now, go to Table V from the appendix to obtain the associated probability. Since the needed area is to the left, that is, \[\begin{align} & P\left( z\gt 1.05 \right)=1-P\left( z\lt1.05 \right) \\ & =1-0.8531 \\ & =0.1469 \end{align}\] Hence, the probability for calcium serum result 10.1 is 0.1469. Section 12 To obtain the blood components that should be cause for concern for Abby, calculate z-score first: \[\begin{align} & z=\frac{\text{data value}-\text{average}}{\text{standard deviation}} \\ & =\frac{253.0-149.5}{24.75} \\ & =4.18 \end{align}\] In this solution, the z-score is greater than 3.50. So, the probability of total cholesterol result 253.0 is out of range. Section 13 To obtain the blood components that should be cause for concern for Abby, calculate z-score first: \[\begin{align} & z=\frac{\text{data value}-\text{average}}{\text{standard deviation}} \\ & =\frac{150-99.5}{49.75} \\ & =1.02 \end{align}\] Now, go to Table V from the appendix to obtain the associated probability, that is, 0.8438. Since the needed area is to the right, so subtract it from 1, that is, \[\begin{align} & P\left( z>1.02 \right)=1-P\left( z<1.02 \right) \\ & =1-0.8438 \\ & =0.1562 \end{align}\] Hence, the probability for triglyceride result 150 is 0.1562. Section 14 To obtain the blood components that should be cause for concern for Abby, calculate z-score first: \[\begin{align} & z=\frac{\text{data value}-\text{average}}{\text{standard deviation}} \\ & =\frac{42.0-92.5}{28.75} \\ & =-1.76 \end{align}\] Now, go to Table V from the appendix to obtain the associated probability. Since the needed area is to the left, that is, \[\begin{align} & P\left( z\gt 3.47 \right)=1-P\left( z\lt 3.47 \right) \\ & =1-0.9997 \\ & =0.0003 \end{align}\] Hence, the probability for LDL/HDL result 150 is 0.0003. Section 17 To obtain the blood components that should be cause for concern for Abby, calculate z-score first: \[\begin{align} & z=\frac{\text{data value}-\text{average}}{\text{standard deviation}} \\ & =\frac{3.15-2.925}{1.2875} \\ & =0.17 \end{align}\] Now, go to Table V from the appendix to obtain the associated probability, that is, 0.8438. Since the needed area is to the right, so subtract it from 1, that is, \[\begin{align} & P\left( z>0.17 \right)=1-P\left( z<0.17 \right) \\ & =1-0.5675 \\ & =0.4325 \end{align}\] Hence, the probability TSH, higher intensity, serum result 3.15 is 0.4325. In the provided study, after all the calculations and analyses, it can be concluded that total cholesterol, cholesterol (LDL), and the ratio of LDL/HDL should be a reason of concern for Abby. All these components have a very low probability or the probability falls out of range. Abby has very low chance to belong to a healthy population. The blood test results concern about assumptions that some of the components of blood are not distributed normally because of their low probability or their probability falls out of range.

Given above.