A screening test for new employees is normally distributed w

A screening test for new employees is normally distributed with a mean = 45 and a standard deviation = 3.

In many situations researchers want to know the cut-off scores between which 95% of test takers will fall and 5% of test takers will fall above or below. What are the lower and upper cut-off scores?

Solution

X -- Scores for a new screening test is N(45, 3)

95% below or above means

P(|Z|<z) = 0.95/2 = 0.475

z value =1.96

Hence x value for higher cut off = 45+3(1.96)

= 45+5.88

= 50.88

Lower cut off score =45-5.88

=39.12