Question

At a high school, the average grade for the English 10 provincial is 64, with a standard deviation of 10. If 20 students scored between 73 and 86 on the exam, how many students took the exam? Use z- scores formulas in your solution for full marks.

Answer 1

118 students

Explanation:

To find the number of students who took the exam, we can use the concept of z-scores and the properties of a standard normal distribution.

Given:

Mean (μ) = 64

Standard Deviation (σ) = 10

We have the following information:

Number of students who scored between 73 and 86 = 20

To calculate the z-score, we use the formula:

z = (x - μ) / σ

For the lower limit of 73:

z1 = (73 - 64) / 10 = 0.9

For the upper limit of 86:

z2 = (86 - 64) / 10 = 2.2

Now, we can look up the z-scores in the standard normal distribution table to find the corresponding cumulative probabilities.

From the z-score table, the cumulative probability for z = 0.9 is approximately 0.8159, and for z = 2.2, it is approximately 0.9857.

To find the number of students who scored between 73 and 86, we subtract the cumulative probabilities:

Number of students = (0.9857 - 0.8159) * N

= 0.1698 * N

Given that this is equal to 20 students, we can set up an equation:

0.1698 * N = 20

Solving for N:

N = 20 / 0.1698

N ≈ 117.74

Since the number of students must be a whole number, we can round it up to the nearest integer:

N ≈ 118

Therefore, approximately 118 students took the English 10 provincial exam.