19M.1.SL.TZ2.T_14
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.
Find the price that is two standard deviations above the mean price.
Find the probability that the price of a kilogram of tomatoes, chosen at random, will be between 2.00 and 3.00 euro.
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.
Markscheme / solution
(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]
4.90 (A1) (C1)
[1 mark]
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 ≤ ≤ 3)” (accept other variables for 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( ≤ ) = 0.2” (accept other variables and strict inequalities).
[2 marks]