Question

The Scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?

a) 62
b) 57
c) 44
d) 40

Answer 1

Answer:

c) 44

Step-by-step explanation:

Mean grade (μ) = 62

Standard deviation (σ) = 11

In a normal distribution, the z-score correspondent to the lower 5-th percentile is approximately z = -1.645.

The z-score, for any given grade 'X' is determined by:

$z=\frac{X-\mu}{\sigma}$

For  z= -1.645:

$-1.645=\frac{X-62}{11}\\X=43.9$

Rounding up to the nearest whole unit. The lowest mark that a student can have and still be awarded a passing grade is 44.