# Exam scores in a MATH 1030 class is approximately normally distributed with mean 87 and standard deviation 5.8. Round answers..?

Exam scores in a MATH 1030 class is approximately normally distributed with mean 87 and standard deviation 5.8. Round answers to the nearest tenth of a percent.

a) What percentage of scores will be less than 92?

b) What percentage of scores will be more than 85?

c) What percentage of scores will be between 83 and 89?

Relevance

http://www.z-table.com/

Find the z-scores for each:

a) (92 - 87) / 5.8

5 / 5.8

25/29

0.86206896551724137931034482758621

z = 0.86, p = 0.8051

80.51%

b)

(85 - 87) / 5.8 =>

-2/5.8 =>

-10/29 =>

-0.34482758620689655172413793103448

1 - z(-0.34) =>

1 - 0.3669 =>

0.6331

63.31%

c)

(83 - 87) / 5.8 =>

-4/5.8 =>

-20/29

(89 - 87) / 5.8 =>

2/5.8 =>

10/29

z(10/29) - z(-20/29) =>

z(0.344) - z(-0.690) =>

0.6331 - 0.2451 =>

0.3880

38.8%

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• Anonymous
6 months ago

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• (a) z = (92 - 87)/5.8 = 0.86207;

normal distribution table says 80.6% of scores are less than this.

(b) z = (85 - 87)/5.8 = -0.34483;

normal distribution table says 13.5% of scores are between z=0 and z=-0.345;

therefore 63.5% of scores are higher than z = -0.345.

(c) z1 = (83 - 87)/5.8 = -0.68966 and

z2 = (89 - 87)/5.8 = +0.34483;

normal distribution table says 13.5% of scores are between z = 0 and z2,

while 25.5% of scores are between z1 and z=0;

therefore 49.0% of scores are between z1 and z2.

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