Suppose SAT Writing scores are normally distributed with a mean of 497 and a standard deviation of 109. A university plans to aw
ard scholarships to students whose scores are in the top 2%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.
1 answer:
Answer:
721.54
Step-by-step explanation:
We have to convert the 2% given in the statement into a z-score, as follows:
P (X> x) = 2% = 0.02, P (Z> z) = 0.02
thus find z such that:
P (Z <z) = 1 - P (Z> z)
P (Z <z) = 1 - 0.02
P (Z <z) = 0.98
we look for what value of z corresponds to in the normal distribution table and it is 2.06
x = m + z * sd
m is mean and sd standard deviation, replacing:
x = 497 + 2.06 * 109
x = 721.54
721.54 would be the minimum score.
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