Easy -1.2 This is a straightforward application of normal distribution requiring a single z-score calculation and multiplication by the sample size. It involves only basic standardization, table lookup, and one arithmetic step with no conceptual challenges or problem-solving required.
2 The volume of ink in a certain type of ink cartridge has a normal distribution with mean 30 ml and standard deviation 1.5 ml . People in an office use a total of 8 cartridges of this ink per month. Find the expected number of cartridges per month that contain less than 28.9 ml of this ink.
Using \(\pm\) standardising formula, no continuity correction, not \(\sigma^2\) or \(\sqrt{\sigma}\)
\(= P(z < -0.733) = 1 - 0.7682\)
M1
Appropriate area \(\Phi\) from standardisation formula \(P(z<\ldots)\) in final probability solution. Must be a probability, e.g. \(1-0.622\) is M0
\(= 0.2318\)
A1
Correct final probability rounding to 0.232. (Only requires M1 not B1 to be awarded)
Number of cartridges is \(their\ 0.2318 \times 8 = 1.85\), so 2 (Also accept 1 but not both)
B1
FT using \(their\) 4 SF (or better) value, ans. rounded or truncated to integer, no approximation indicated
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(<28.9) = P\left(z < \frac{28.9-30}{1.5}\right)$ | B1 | Using $\pm$ standardising formula, no continuity correction, not $\sigma^2$ or $\sqrt{\sigma}$ |
| $= P(z < -0.733) = 1 - 0.7682$ | M1 | Appropriate area $\Phi$ from standardisation formula $P(z<\ldots)$ in final probability solution. Must be a probability, e.g. $1-0.622$ is M0 |
| $= 0.2318$ | A1 | Correct final probability rounding to 0.232. (Only requires M1 not B1 to be awarded) |
| Number of cartridges is $their\ 0.2318 \times 8 = 1.85$, so 2 (Also accept 1 but not both) | B1 | FT using $their$ 4 SF (or better) value, ans. rounded or truncated to integer, no approximation indicated |
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2 The volume of ink in a certain type of ink cartridge has a normal distribution with mean 30 ml and standard deviation 1.5 ml . People in an office use a total of 8 cartridges of this ink per month. Find the expected number of cartridges per month that contain less than 28.9 ml of this ink.\\
\hfill \mbox{\textit{CAIE S1 2019 Q2 [4]}}