SPM 2016 Additional Mathematics (Forecast Paper)
Answer any four questions from this section.Question 10
(a) 20% of the students in SMK Bukit Bintang are cycling to school. If 9 pupils from the school are chosen at random, calculate the probability that
(i) exactly 3 of them are cycling to school,
(ii) at least a student is cycling to school.
(b) The volume of 800 bottles of fresh milk produced by a factory follows a normal distribution with a mean of 520 ml per bottle and variance of 1600 ml2.
(i) Find the probability that a bottle of fresh milk chosen in random has a volume of less than 515 ml.
(ii) If 480 bottles out of 800 bottles of the fresh milk have volume greater that k ml, find the value of k.
Answer and Solution:
X ~ Students in SMK Bukit Bintang who are cycling to school
X ~ B (n, p)
X ~ B (9, 0.2)
P (X = r) = nCr. pr. qn-r
Probability, exactly 3 students are cycling to school
P (X = 3) = 9C3 (0.2)3 (0.8)6
At least a student is cycling to school
= 1 – P(X = 0)
= 1 – 9C0 (0.2)0 (0.8)9
m = 520 ml
σ2 = 1600 ml2
σ = 40
Let X represents volume of a bottle of fresh milk.
X ~ N (520, 1600)
P(X < 515)
= P(Z < – 0.125)
= P(Z > 0.125)