Question

Drug content assessment. Scientists at GlaxoSmithKlineMedicines Research Center used high-performance liquidchromatography (HPLC) to determine the amountof drug in a tablet produced by the company (Analytical

Chemistry, Dec. 15, 2009). Drug concentrations (measuredas a percentage) for 50 randomly selected tablets are listedin the table below and saved in the accompanying file.

a. Descriptive statistics for the drug concentrations areshown at the top of the XLSTAT printout on the nextpage. Use this information to assess whether the dataare approximately normal.

b. An XLSTAT normal probability plot follows. Use thisinformation to assess whether the data are approximatelynormal.

91.28 92.83 89.35 91.90 82.85 94.83 89.83 89.00 84.62

86.96 88.32 91.17 83.86 89.74 92.24 92.59 84.21 89.36

90.96 92.85 89.39 89.82 89.91 92.16 88.67 89.35 86.51

89.04 91.82 93.02 88.32 88.76 89.26 90.36 87.16 91.74

86.12 92.10 83.33 87.61 88.20 92.78 86.35 93.84 91.20

93.44 86.77 83.77 93.19 81.79

Descriptive statistics(Quantitative data)
Statistic	Content
Nbr.of Observation	50
Minimum	81.79
Maximum	94.83
1st Quartile	87.2725
Median	89.375
3rd Quartile	91.88
Mean	89.2906
Variance(n-1)	10.1343
Standard deviation(n-1)	3.1834

Short answer

a. The data is approximately normal.

b. The data is approximately normal.

Step-by-step solution

Given information

Drug concentrations (measured as a percentage) for 50 randomly selected tablets are listed as follows:

The first quantile is 87.2725

$Q_1=87.2725$

The third quantile is 91.88

$Q_2=91.88$

The Standard deviation $s=3.1834$.

Checking of normality using a numerical measure

a.

$$\begin{gathered} \frac{IQR}{s}=\frac{Q_3-Q_1}{s} \\ =\frac{91.88-87.2725}{3.1834} \\ =1.4474 \end{gathered}$$

Here, the value of IQR/s is approximately 1.3

So, we can conclude that the data is approximately normal.

Checking of normality using graph

b.

From the graph, it is seen that approximately all data points fall into a straight line.

So, we can conclude that the data is approximately normal.