1. Find the value z of a standard normal variable Z that satisfies each of the f

Question

1. Find the value z of a standard normal variable Z that satisfies each of the following conditions.

30% of observations fall above z

2. There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores for more than 1 million students in a recent high school graduating class was roughly normal with mean = 20.8 and standard deviation = 4.8. SAT scores are reported on a scale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughly normal with mean = 1026 and standard deviation = 209.

How well must Abigail do on the SAT in order to place in the top 16% of all students? (Round your answer to the nearest whole number.)

Please show steps and explain.

Explanation / Answer

30% value of fall above z that means 70% fall below it hence , prob of 0.7 is calculated using z score calculatop Through the Z score calculator ans comes out to be 0.524

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