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

Find the value of \(a\).

Estimate the interquartile range of the distribution.

\(0.5{\text{ }}\left( {50\% ,{\text{ }}\frac{1}{2}} \right)\)     (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).

OR

\(434 - 366.275 \ldots \)     (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.

OR

     (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]