Question

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

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 %