The scores of a high school entrance exam are approximately normally distributed with a given mean = 82.4 and standard deviation = 3.3. What percentage of the scores are between 75.8 and 89?

Question

Mathematics

Alessandra Rocha

22 February, 11:06

The scores of a high school entrance exam are approximately normally distributed with a given mean = 82.4 and standard deviation = 3.3. What percentage of the scores are between 75.8 and 89?

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Sam Greer · Answer 1

P (75.8 < X < 89) = P (X < 89) - P (X < 75.8) = P (z < (89 - 82.4) / 3.3) - P (z < (75.8 - 82.4) / 3.3) = P (z < 2) - P (z < - 2) = 2P (z < 2) - 1 = 2 (0.97725) - 1 = 1.9545 - 1 = 0.9545