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(X≥40)=P(Z≥40−568) =P(Z≥−2) =1−P(Z≥2) =1−0.02275 =0.9773Number of students who pass the test=0.9773×300=293(b) Let the minimum mark to obtain grade A be kP(X≥k)=0.12P(Z≥k−568)=0.12 k−568=1.17 k=(1.17)(8)+56=65.36
Thus, the minimum mark to obtain grade A is 66.
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(X≥40)=P(Z≥40−568) =P(Z≥−2) =1−P(Z≥2) =1−0.02275 =0.9773Number of students who pass the test=0.9773×300=293(b) Let the minimum mark to obtain grade A be kP(X≥k)=0.12P(Z≥k−568)=0.12 k−568=1.17 k=(1.17)(8)+56=65.36
Thus, the minimum mark to obtain grade A is 66.