A mandatory competency test for second-year high school students has a normal distribution with a mean of 485 and a standard deviation of 85. a) The top 2% 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?
Solution:-
Given that,
mean =
= 485
standard deviation =
= 85
a) Using standard normal table,
P(Z > z) = 2%
= 1 - P(Z < z) = 0.02
= P(Z < z) = 1 - 0.02
= P(Z < z ) = 0.98
= P(Z < 2.05 ) = 0.98
z = 2.05
Using z-score formula,
x = z *
+
x = 2.05 * 85 + 485
x = 659.25
x = 659
b) Using standard normal table,
P(Z < z) = 4%
= P(Z < z ) = 0.04
= P(Z < -1.75 ) = 0.04
z = -1.75
Using z-score formula,
x = z *
+
x = -1.75 * 85 + 485
x = 336.25
x = 336
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