Question

A mandatory competency test for high school sophomores has a normal distribution with a mean of and a standard deviation of . Round the final answers to the nearest whole number and intermediate -value calculations to decimal places. (a)The top of students receive . What is the minimum score you would need to receive this award?

Answer 1

The minimum scores are:

a) 674 is the minimum score necessary to receive $500

b) 306 is the minimum score to stay out of summer school

How to find the z-score?

a) 1 - 0.04 = 0.96, a z-score of 1.75 corresponds to 0.96 probability

1.75 = (X - 490)/105

X - 490 = 1.75 * 105

X = 183.75

X = 183.75 + 490

X = 673.75

674 is the minimum score necessary to receive $500

b) A z-score of -1.75 corresponds to 0.04 probability

-1.75 = (X - 490) / 105

X - 490 = -1.75 * 105

X = -183.75

X = -183.75 + 490

X = 306.25

306 is the minimum score to stay out of summer school