According to an official in the quality assurance department of a can manufacturing business, the standard deviation of a 340 ml can is 2,74 ml - NSC Mathematics - Question 2 - 2016 - Paper 2

To find the standard deviation, we first need to calculate the variance. The formula for variance is:

$\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{N}$

Where:

• $x_i$ are the individual measurements.
• $\bar{x}$ is the mean calculated earlier.
• $N$ is the total number of cans.

After calculating the variance, we take the square root to find the standard deviation: $\sigma = \sqrt{ \sigma^2 } = 2.71 \text{ ml}$

To find the percentage of data within one standard deviation from the mean, we use the interval:

$[\bar{x} - \sigma, \bar{x} + \sigma] = [338.6 - 2.71, 338.6 + 2.71] = [335.89, 341.31]$

Next, we check how many of the measured volumes fall within this range:

• The volumes within this interval must be counted, and then we calculate the percentage:
• Let’s say there are 15 values within that range.

Then: $\text{Percentage} = \frac{15}{20} \times 100 = 75\%$