In: Statistics and Probability
A survey indicates that approximately 67% of adults oppose raising the Medicare eligibility age from 65 to 67. If 80 adults are randomly selected, find the probability that the number who oppose raising the age, will be a) at most 60; b) more than 40; c) exactly 50?
(a)
n = 80
p = 0.67
q = 1- p = 0.33
= mean = np = 80 X 0.67 = 53,6'
To find P(X60):
Applying Continuity Correction:
To find P(X<60.5):
Z = (60.5 - 53.6)/4.2057 = 1.64
Table of Area Under Standard Normal Curve gives area = 0.4495
So,
P(X60) = 0.5 + 0.4495 = 0.9495
So,
Answer is:
0.9495
(b)
(a)
n = 80
p = 0.67
q = 1- p = 0.33
= mean = np = 80 X 0.67 = 53,6'
To find P(X>40):
Applying Continuity Correction:
To find P(X>40.5):
Z = (40.5 - 53.6)/4.2057 = - 3.11
Table of Area Under Standard Normal Curve gives area = 0.4991
So,
P(X>40) = 0.5 + 0.4991 = 0.9991
So,
Answer is:
0.9991
(c)
(a)
n = 80
p = 0.67
q = 1- p = 0.33
= mean = np = 80 X 0.67 = 53,6'
To find P(X=50):
Applying Continuity Correction:
To find P(49.5<X<50.5):
Case1 : For X from 49.5 to mid value:
Z = (49.5 - 53.6)/4.2057 = - 0.97
Table of Area Under Standard Normal Curve gives area = 0.3340
Case2 : For X from 50.5 to mid value:
Z = (50.5 - 53.6)/4.2057 = - 0.74
Table of Area Under Standard Normal Curve gives area = 0.2704
So,
P(X=50) = 0.3340- 0.2704 = 0.0636
So,
Answer is:
0.0636