A mandatory competency test for high school sophomores has a normal distribution

Question

A mandatory competency test for high school sophomores has a normal distribution with a mean of 485 and a standard deviation of 97. Round the final answers to the nearest whole number and intermediate z-value calculations to 2 decimal places a. The top 6% of students receive S500. What is the minimum score you would need to receive this award? The minimum score needed to receive the award is b. The bottom 4.5% of students must go to summer school. What is the minimum score you would need to stay out of this group? The minimum score needed to stay out of this group is

Explanation / Answer

for top 6% ; at 94th percentile z =1.55

hence corresponding minimum score =mean +z*std deviaiton =485+1.55*97=~ 635

b)

for bottom 4.5% ; at 4.5th percentile z =-1.70

hence corresponding minimum score =mean +z*std deviaiton =485-1.70*97=~320

(please revert as z value has been taken with 2 decimals only. answer will slightly vary if z value taken with more significant digits)

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