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.
Accepted Solution
A:
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