In her MAT135 class, professor Alayeb found that the mean score of the first exam was 96. Suppose that the scores are normally distributed with a standard deviation of 19 points.

Question

What is the probability that a randomly selected score is less than 71? 

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What is the probability that a randomly selected score is more than 82?

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what is the probability that a randomly selected score is between 71 and 82 ? 

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Answer 1

mean = 96= xbar

standard deviation = s = 19

P(x<71)=?

z= (71-96)/19= -25/19 = about - 1.316 = over 1 standard deviation below the mean, < (1-.68)/2 = .16

and greater than 2 s below the mean = (1-.95)/2= .05/2 = .025, by the empirical rule 68-95-99.7

.024 < P(x<71) < .16 maybe about (.024+.16)/2=.18/2 = roughly .09

look up z on z tables or z calculator to find area = probability =.0941 = 9.41 % chance less than 71

P(x>82)

z= (81-96)/19=- 15/19 =- .7895

look it up on z tables

area = probability = .2149 =21.49% chance less than 82

.7851 = 78.51% greater than 82

P(71<x<82)=.2149-.0941 = .1108 = 11.08 % chance between 71 and 82