Question

In a math aptitude test, student scores are found to be normally distributed having mean as 45 and standard deviation 5. What percentage of students have scores -

(i) more than the mean score?

(ii) between 30 and 50?

Answer 1

X = scores of students,

(i) When X = 45, Z = 0

P (X > 45) = P (Z > 0) = 0.5

⇒ 50% students scored more than the mean score

(ii) When X = 30, = −3 and when X = 50, Z = 1

P (30 < X < 50) = P ( -3 < Z < 1) = P (-3 < Z ≤ 1)

= P ( − 3 < Z ≤ 0) + P (0 ≤ Z < 1)

= P (0 ≤ Z < 3) + P (0 ≤ Z < 1)

= 0.4987 + 0.3413 = 0.84

⇒ 84% students scored between 30 and 50 marks