Question

In: Statistics and Probability

A survey indicates that approximately 67% of adults oppose raising the Medicare eligibility age from 65...

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?

Solutions

Expert Solution

(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


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