Question

1. Find the value z of a standard Normal variable Z that satisfies each of the following conditions. (If you use Table A, report the value of z that comes closest to satisfying the condition.) In each case, sketch a standard Normal curve with your value of z marked on the axis.

38% of the observations fall below z

70% of the observations fall above z

2.) Jorge scores 2090 on the SAT. Assuming that both tests measure the same thing, what score on the ACT is equivalent to Jorge’s SAT score?

3.) Reports on a student’s ACT or SAT results usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than or equal to this one. Renee scores 2050 on the SAT. What is her percentile?

4.)What SAT scores make up the top 12% of all scores?

Answer 1

Q 1)

a) 38% of the observations fall below Z

From standard normal table , the value of Z corresponding to the area 0.12 is -0.305

Answer: Z₁ = -0.31

b) 70% of the observations fall above z

From Standard normal table, the value of Z corresponding to the area 0.20 is -0.524

Answer: Z₁ = -0.524