Question

4. A normal distribution has a mean = 60 and SD = 10. For this distribution, find each of

the following probability values:

4.1. P(X> 65) = ___________________ 4.3. P(X < 75) =________________

4.2. P(X < 80) = ___________________ 4.4. P(55 < X < 85) =____________

Answer 1

(4.1)

= 60

= 10

To find P(X>65):

Z = (65 - 60)/10

= 0.50

Table of Area Under Standard Normal Curve gives area = 0.1915

So,

P(X>65) = 0.5 - 0.1915 = 0.3085

So,

Answer is:

0.3085

(4.2)

= 60

= 10

To find P(X<80):

Z = (80 - 60)/10

= 2.00

Table of Area Under Standard Normal Curve gives area = 0.4772

So,

P(X<80) = 0.5 + 0.4772 = 0.9772

So,

Answer is:

0.9772

(4.3)

= 60

= 10

To find P(X<75):

Z = (75 - 60)/10

= 1.50

Table of Area Under Standard Normal Curve gives area = 0.4332

So,

P(X<75) = 0.5 + 0.4332 = 0.9332

So,

Answer is:

0.9332

(4.4)

= 60

= 10

To find P(55<X<85):

Case 1: For X 55 to mid value:

Z = (55 - 60)/10

= - 0.50

Table of Area Under Standard Normal Curve gives area = 0.1915

Case 2: For X from mid value to 85:

Z = (85 - 60)/10

= 2.50

Table of Area Under Standard Normal Curve gives area = 0.4938

So,

P(55<X<85) = 0.1915 + 0.4938 = 0.6853

So,

Answer is:

0.6853