19M.1.SL.TZ2.T_14

pestleMathematicsAASLPaper 119M· sl-4-3-mean-median-mode-mean-of-grouped-data-standard-deviation-quartiles-iqrsource ↗

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.

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]

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]

Markscheme / solution

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]

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]

Examiners’ report

[N/A]

a.ii.

[N/A]