Consider a value to be significantly low if its z score less than or equal to minus−2 or consider a value to be significantly high if its z score is greater than or equal to 2.
A test is used to assess readiness for college. In a recent year, the mean score was 22.5 and the standard deviation was 5.1. Identify the scores that are significantly low or significantly high.
the z-score is given by: z-score=(x-μ)/σ where: x=score μ=mean=22.5 σ=std deviation=5.1 given that the z-score is -2, then the lowest cost will be: -2=(x-22.5)/5.1 solving for x we get: -10.2=x-22.5 x=-10.2+22.5 x=12.3 therefor the lowest score is 12.3
Given that the z-score is 2 when the score is highest, then highest score will be: 2=(x-22.5)/5.1 10.2=x-22.5 x=10.2+22.5 x=32.7 therefore the highest score is 32.7
