SOLUTION: A mandatory competency test for high school sophomores has a normal distribution with a mean of 490 and a standard deviation of 105. Round the answers to the nearest whole number a

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Question 1081763: A mandatory competency test for high school sophomores has a normal distribution with a mean of 490 and a standard deviation of 105. Round the answers to the nearest whole number and intermediate z-value calculations to 2 decimal places.
a) The top 4% of students receive $500. What is the minimum score you would need to receive this award.
b) The bottom 4% of students must go to summer school. What is the minimum score you would need to stay out of this group.

Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
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 = 183.75
X = 183.75 + 490 = 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 = -183.75
X = -183.75 + 490 = 306.25
306 is the minimum score to stay out of summer school