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Date May 2017 Marks available 1 Reference code 17M.1.SL.TZ2.T_11
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Write down Question number T_11 Adapted from N/A

Question

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]
a.

Find the value of a .

[2]
b.

Estimate the interquartile range of the distribution.

[3]
c.

Markscheme

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

0.5   ( 50 % ,   1 2 )     (A1)     (C1)

[1 mark]

a.

P ( X > a ) = 0.25 OR 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  (g)  ( 433.724  (g) )     (A1)     (C2)

[2 marks]

b.

33.7244 × 2     (A1)(ft)(M1)

 

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

 

OR

434 366.275     (A1)(ft)(M1)

 

Note:     Award (A1)(ft) for their 366.275   ( 366 ) seen, (M1) for difference between their answer to (b) and their 366.

 

OR

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

 

Note:     Award (A1)(ft) for their 366.275   ( 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]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
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Topic 4—Statistics and probability

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