Study text: "Essential Mathematics and Statistics for Science", 2nd Edition,

G Currell & A A Dowman, Wiley-Blackwell, 2009

G Currell & A A Dowman, Wiley-Blackwell, 2009

- A specific sample of blood has a true alcohol level of 80 mg per 100mL of blood.

The experimental measurement has random variations, and the graph shows the probabilities that a single measurement will record a value within the ranges shown.

The distribution of values follow a Normal (or Gaussian) distribution with a standard deviation of 2.0 mg per 100mL.

Using the data in the graph calculate the probability that a single measurement would record a value**greater than**82.0 mg per 100mL.- 0.0918
- 0.1586
- 0.3172
- 0.3414

- The lengths of fish in a breeding tank give a Normal distribution as shown in the graph.

For a Normal (or Gaussian) distribution,

i) there are approximately 3 standard deviations from the centre to each tail, and/or

ii) the width at half height is approximately equal to 2.4 standard deviations.

Using the above information, estimate the**standard deviation**of the distribution in the graph. Select the closest value.- 1.8
- 2.0
- 2.4
- 3.0

- The graph shows the probability, for a Normal distribution, of obtaining a value within each of the ranges marked in multiples of the standard deviation,
*σ*.

Select ALL of the statements that are correct.

(Click here for the Video Answer)**The probability of obtaining a value:** - Select ALL of the following statements that are true:

(Click here for the Video Answer) - The graph shows the probability, for a Normal distribution, of obtaining a value within each of the ranges marked in multiples of the standard deviation,
*σ*.

If the true alcohol level in a sample of blood is 78 mg per 100mL and the unbiased experimental measurement has a standard deviation uncertainty of 2 mg per 100mL, what is the probability that a single measurement will give a value that is greater than 80 mg per 100mL?- 0.3413
- 0.3174
- 0.1587
- 0.1574

- The true concentration,
*µ*, of sodium in a sample of mineral water is given by*µ*= 8.2 mg L^{-1}.

An unbiased experimental measurement, that has a standard deviation uncertainty,*σ*= 0.3 mg L^{-1}, is repeated many times.

Select ALL of the statements that are correct.

(Click here for the Video Answer)**It is possible to state that 95% of the measured values can be expected to fall -**