Discussion
A cement has a mean strength of 50 megapascals with a standard deviation of 3. Roughly what proportion of results would fall below 44 megapascals?
Answer: A
Correct answer: about 2.5 per cent
44 MPa lies two standard deviations below the mean: \[ z = \frac{44-50}{3} = -2. \] For a normal distribution about 2.3 per cent of results fall below \( -2\sigma \), so roughly 2.5 per cent. The 16 per cent offered is the proportion below one standard deviation, which is what results from dividing by 6 instead of 3.
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