17M.1.SL.TZ2.T_11

pestleMathematicsAASLPaper 117M· sl-4-9-normal-distribution-and-calculationssource ↗

The mass of a certain type of Chilean corncob follows a normal distribution with a mean of 400 grams and a standard deviation of 50 grams.

A farmer labels one of these corncobs as premium if its mass is greater than $a$ grams. 25% of these corncobs are labelled as premium.

Write down the probability that the mass of one of these corncobs is greater than 400 grams.

[1]

Find the value of $a$ .

[2]

Estimate the interquartile range of the distribution.

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$0.5{\text{ }}\left( {50\% ,{\text{ }}\frac{1}{2}} \right)$ (A1) (C1)

[1 mark]

${\text{P}}(X > a) = 0.25$ $\,\,\,$ OR $\,\,\,$ ${\text{P}}(X < a) = 0.75$ (M1)

Note: Award (M1) for a sketch of approximate normal curve with a vertical line drawn to the right of the mean with the area to the right of this line shaded.

$a = 434{\text{ (g) }}\left( {433.724 \ldots {\text{ (g)}}} \right)$ (A1) (C2)

[2 marks]

$33.7244 \ldots \times 2$ (A1)(ft)(M1)

Note: Award (A1)(ft) for $33.7244 \ldots {\text{ }}({\text{or }}433.7244 \ldots {\text{ }} - {\text{ }}400)$ seen, award (M1) for multiplying their 33.7244… by 2. Follow through from their answer to part (b).

$434 - 366.275 \ldots$ (A1)(ft)(M1)

Note: Award (A1)(ft) for their $366.275 \ldots {\text{ }}(366)$ seen, (M1) for difference between their answer to (b) and their 366.

M17/5/MATSD/SP1/ENG/TZ2/11.c/M (A1)(ft)(M1)

Note: Award (A1)(ft) for their $366.275 \ldots {\text{ }}(366)$ seen. Award (M1) for correct symmetrical region indicated on labelled normal curve.

67.4 (g) (A1)(ft) (C3)

Note: Accept an answer of 68 from use of rounded values. Follow through from part (b).

[3 marks]

Examiners’ report

[N/A]