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? give the answer that is closest to the exact number.

Question

Mathematics

Hailee Booth

17 July, 10:40

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? give the answer that is closest to the exact number.

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Answers (1)

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Ernest Pham · Answer 1

The lowest score will be obtained as follows:

the z-score is given by:

z = (x-μ) / σ

where:

σ-standard deviation

μ - mean

we are required to evaluate for x, given that P (x
The value of z that corresponds to 5% will be:

z=-1.65

thus plugging our values we obtain:

-1.65 = (x-62) / 11

solving for x we get:

-18.15=x-62

thus

x=-18.15+62

x=43.85

x~44

Thus the lowest score is 44