Question

The median of the results was 80 points out of 100, with a standard deviation of 6 points. Which of the following numbers is closest to the number of students that got more than 86 but less than 92 points? 1 3 7 9

Answer 1

3

Explanation

z-score of 86 = 1

z-score of 92 = 2

P(1 < Z < 2) = 0.1359

Number of students: 0.1359 x 22 = 3

Answer 2

We want to find P-value of (86<X<92)

Start by working out the z- score for X=86 and X=92

for X = 86
z-score = [86-80]/6 = 1

for X = 92
z-score = [92-80]/6 = 2

P(1<Z<2) = P(Z<2) - P(Z<1)

Read P(Z<2) and P(Z<1) on the z-table
P(1<Z<2) = 0.9772 - 0.8413 = 0.1359

Probability of a student achieve a mark between 86 and 92 is 0.1359 and out of 100, this is 0.1359 × 100 = 13.59

The closest number of student is = 9 students