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Date May 2019 Marks available 2 Reference code 19M.1.SL.TZ2.T_14
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number T_14 Adapted from N/A

Question

The price per kilogram of tomatoes, in euro, sold in various markets in a city is found to be normally distributed with a mean of 3.22 and a standard deviation of 0.84.

On the following diagram, shade the region representing the probability that the price of a kilogram of tomatoes, chosen at random, will be higher than 3.22 euro.

[1]
a.i.

Find the price that is two standard deviations above the mean price.

[1]
a.ii.

Find the probability that the price of a kilogram of tomatoes, chosen at random, will be between 2.00 and 3.00 euro.

[2]
b.

To stimulate reasonable pricing, the city offers a free permit to the sellers whose price of a kilogram of tomatoes is in the lowest 20 %.

Find the highest price that a seller can charge and still receive a free permit.

[2]
c.

Markscheme

    (A1)   (C1)

Note: Award (A1) for vertical line drawn at the mean (3.22 does not have to be seen) and correct region shaded.

[1 mark]

a.i.

4.90     (A1)   (C1)

[1 mark]

a.ii.

0.323  (0.323499…; 32.3 %)     (A2)   (C2)

Note: If final answer is incorrect, (M1)(A0) may be awarded for correct shaded area shown on a sketch, below, or for a correct probability statement “P(2 ≤ X ≤ 3)” (accept other variables for X or “price” and strict inequalities).

[2 marks]

b.

2.51  (2.51303…)       (A2)   (C2)

Note: If final answer is incorrect, (M1)(A0) may be awarded for correct shaded area shown on a sketch, below, or for a correct probability statement “P( X a ) = 0.2” (accept other variables and strict inequalities).

[2 marks]

c.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
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Topic 4—Statistics and probability » SL 4.9—Normal distribution and calculations
Topic 4—Statistics and probability

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