Question

A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $97 and a standard deviation of $10. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $87

Answer 1

The percentage of homes will have a monthly utility bill of more than $87

P(X>87) = 0.8413 X 100 = 84.13%

Explanation:

Explanation:-

Given Mean of the Population =97

Standard deviation of the Population = 10

Let 'X' be the random variable in normal distribution

`z=(x-mean)/(S.D)`

`z=(87-97)/(10)`

Z= -1

The probability that homes will have a monthly utility bill of more than $87

P(X>87) = P( Z>-1) = 0.5 + A(-1)

= 0.5 + A(1) (∵A(-1)=A(1)

=0.5 + 0.3413

= 0.8413

The percentage of homes will have a monthly utility bill of more than $87

P(X>87) = 0.8413 X 100 = 84.13%