Question

Distribution of the amount of monthly utility bill of a 3-bedroom house using gas or electric energy had μ = $150 and σ = $10.

(i) What percentage of homes will have a monthly utility bill between $130 and $170?

(ii) What percentage of homes will have a monthly utility bill of less than $120 or more than $180?

Answer 1

(i)

$\mu$ = 150

$\sigma$ = 10

To find P(130< X < 170):

Case 1:For X from 130 to mid value:
Z = (130- 150)/10 = - 2

Table of Area Under Standard Normal Curve gives area = 0.4772

Case 2 :For X from mid value to 170:
Z = (170- 150)/10 = 2

Table of Area Under Standard Normal Curve gives area = 0.4772

So,

P(130 < X < 170) = 0.4772 X 2 = 0.9544 = 95.44 %

So,

Answer is:

95.44 %

(ii)To find P(X<120 OR X > 180):

Case 1:For X <120:
Z = (120- 150)/10 = - 3

Table of Area Under Standard Normal Curve gives area = 0.4987

So,

P(X<120) = 0.5 - 0.4987 = 0.0013

Case 2: For X > 180:
Z = (180- 150)/10 = 3

Table of Area Under Standard Normal Curve gives area = 0.4987

So,

P(X>180) = 0.5 - 0.4987 = 0.0013

So,

P(X<120 OR X> 180) =0.0013 X 2 = 0.0026 = 0.26 %

So,

Answer is:

0.26 %