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.

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<X)=0.05
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