Question

Given a Normal distribution with mean = 150 and sigma = 10,

A. What is the probability that X > 146?

B. What is the probability that X < 154?

C. What is the probability that 146 < X < 154?

D. 80% of the values are less than what X value?

Answer 1

(A)

= 150

= 10

To find P(X>146):

Z = (146 -150)/10

= - 0.40

Table gives area = 0.1554

So,

P(X>146) = 0.5 + 0.1554 = 0.5554

So,

Answer is:

0.5554

(B)
To find P(X<154):
Z = (154 - 150)/10

= 0.40

Table gives area = 0.1554

So,\P(X<154) = 0.5 + 0.1554 = 0.5554

So,

Answer is:

0.5554

(C)

To find P(146<X<154):

Case 1: For X from 146 to mid value:

Z = (146 -150)/10

= - 0.40

Table gives area = 0.1554

Case 2: For X from mid value to 154:

Z = (154 - 150)/10

= 0.40

Table gives area = 0.1554

So,

P(146<X<154) = 2 X 0.1554 = 0.3108

So,

Answer is:

0.3108

(D) 80% corresponds to area = 0.80 - 0.50 = 0.30

Table gives Z = 0.84

So,

Z = 0.84 = (X - 150)/10

So,

X = 150 + (10 X 0.84)

   = 158.40

So,

Answer is:

158.40