Question

for a normal distribution with mean 100 and standard deviation of 20, calculate: a) the percentage...

for a normal distribution with mean 100 and standard deviation of 20, calculate: a) the percentage of the values between 100 and 120 b) the percentage of the values between 60 and 80 c) the percentage of the values between 80 and 140

Homework Answers

Answer #1

(a)

= mean = 100

= SD = 20

To find P(100 < X < 120):

Z = (120 - 100)/20 = 1

Table of Area Under Standard Normal Curve gives area = 0.3413 = 34.13 %

So,

Answer is:

34.13 %

(b)

To find P(60 < X < 80):

Case 1: for X from 60 to mid value:

Z = (60 - 100)/20 = - 2
Table gives area = 0.4772

Case 2: For X from 80 to mid value:
Z = (80 - 100)/20 = - 1

Table gives area = 0.3413

So,

P(60 < X < 80) = 0.4772 - 0.3413 = 0.1359 = 13.59 %

So,

Answer is:

13.59 %

(c)

P(80 < X < 140):

Case 1: For X from 80 to mid value:
Z = (80 - 100)/20 = - 1

Table gives area = 0.3413

Case 2: For X from mid value to 140:

Z = (140-100)/20 = 2

Table gives area = 0.4772

So,

P(80 < X < 140) = 0.0.3413 + 0.4772 = 0.8185 = 81.85 %

So,

Answer is:

81,85 %

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