Long Questions (Question 7)


Question 7:
In a boarding school entry exam, 300 students sat for a mathematics test. The marks obtained follow a normal distribution with a mean of 56 and a standard deviation of 8.

(a) Find the number of students who pass the test if the passing mark is 40.

(b) If 12% of the students pass the test with grade A, find the minimum mark to obtain grade A.

Solution:
Let X=marks obtained by studentsX~N(56,82)(a) P(X40)=P(Z40568)   =P(Z2)   =1P(Z2)   =10.02275   =0.9773Number of students who pass the test=0.9773×300=293(b) Let the minimum mark to obtain grade A be kP(Xk)=0.12P(Zk568)=0.12 k568=1.17  k=(1.17)(8)+56=65.36

Thus, the minimum mark to obtain grade A is 66.