The serum potassium is measured in 1,000 patients taking an ACE inhibitor. The mean potassium is 4.6 mmol/l with a standard deviation of 0.3 mmol/l. Which one of the following statements is correct?

95% of values lie between 4.5 and 4.75 mmol/l

95.4% of values lie between 4.3 and 4.9 mmol/l

99.7% of values lie between 4.0 and 5.2 mmol/l

68.3% of values lie between 4.5 and 4.75 mmol/l

68.3% of values lie between 4.3 and 4.9 mmol/l

#### Normal distribution

The normal distribution is also known as the Gaussian distribution or ‘bell-shaped’ distribution. It describes the spread of many biological and clinical measurements

Properties of the Normal distribution

- symmetrical i.e. Mean = mode = median
- 68.3% of values lie within 1 SD of the mean
- 95.4% of values lie within 2 SD of the mean
- 99.7% of values lie within 3 SD of the mean
- this is often reversed, so that within 1.96 SD of the mean lie 95% of the sample values
- the range of the mean - (1.96 *SD) to the mean + (1.96 * SD) is called the 95% confidence interval, i.e. If a repeat sample of 100 observations are taken from the same group 95 of them would be expected to lie in that range

Standard deviation

- the standard deviation (SD) is a measure of how much dispersion exists from the mean
- SD = square root (variance)