19M.2.AHL.TZ2.H_2
Timmy owns a shop. His daily income from selling his goods can be modelled as a normal distribution, with a mean daily income of $820, and a standard deviation of $230. To make a profit, Timmy’s daily income needs to be greater than $1000.
Calculate the probability that, on a randomly selected day, Timmy makes a profit.
The shop is open for 24 days every month.
Calculate the probability that, in a randomly selected month, Timmy makes a profit on between 5 and 10 days (inclusive).
Markscheme / solution
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
X ~ N(820, 2302) (M1)
Note: Award M1 for an attempt to use normal distribution. Accept labelled normal graph.
⇒P(X > 1000) = 0.217 A1
[2 marks]
Y ~ B(24,0.217...) (M1)
Note: Award M1 for recognition of binomial distribution with parameters.
P(Y ≤ 10) − P(Y ≤ 4) (M1)
Note: Award M1 for an attempt to find P(5 ≤ Y ≤ 10) or P(Y ≤ 10) − P(Y ≤ 4).
= 0.613 A1
[3 marks]