# Test Yourself

## True or False

### Question 1

A linear transformation might stretch or shrink the scale of distribution but it does not change the shape of a distribution.

### Question 2

A z-transformation measures the distance of each observation from the mean in units of standard deviation.

### Question 3

A z-score can be converted to a percentile rank.

### Question 4

To convert a value to a z-score we subtract the mean and divide by the standard deviation

### Question 5

Z-scores are useful when you wish to compare two variables with different measurement units. For example, the exam score from an English and Maths exam.

### Question 6

A z-transformation standardises values to have a mean of 1 and SD of 1

### Question 7

Z-scores can be related to the standard normal distribution to work out the probability that a randomly selected observation will have a value as extreme as that observed.

### Question 8

Z-scores can be useful to flag outliers, often observations more than 1 SD from the mean are classified as an outlier.

### Question 9

The standard normal distribution (and hence z-scores) are used to estimate 95% reference ranges

### Question 10

The 68-95-99.7 rule states that when a variable is normally distributed, approximately, 68, 95 and 99.7% of observations will lie with 1 2 or 3 standard deviations of the mean.

## DropDown Activity

The distribution of systolic blood pressure for a random sample of individuals extracted from a population of heavy smokers had a sample mean of 147mmHg and a standard deviation of 25mmHg

What is the approximate 95% reference range for SBP in this study?

## True or False

A 95% reference range for SBP in smokers is found to be 97 to 197mmHg. How would you interpret this range?
Please indicate which of the following statements are acceptable.

### Question 1

If I picked an individual at random from this population, there’s a 95% chance they’d have a blood pressure within this range.

### Question 2

Blood pressure within this range is normal.

### Question 3

5% of smokers would be expected to have a systolic blood pressure outside this range.

### Question 4

95% of smokers in  this population would be expected to have a blood pressure within this range.