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

Question

Mathematics

Chen

7 October, 21:52

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

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Answers (1)

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Melany Duran · Answer 1

Mean, m=82.4

standard deviation, sigma=3.3

Need proportion of sample between 75.8 and 89.

first calculate Z-scores of 75.8 and 89

Z (75.8) = (75.8-82.4) / 3.3=-2

Z (89) = (89-82.4) / 3.3=2

So

P (75.8
=P (-2
=P (Z<2) - P (Z<-2)

=0.9772-0.0227

=0.9545