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 $92 and a standard deviation of $13. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $79? a. approximately 34%b. approximately 16%c. approximately 95%d. approximately 84%

Answer 1

Answer:

option d) approximately 84%

Explanation:

Data provided in the question:

Mean, m = $92

Standard deviation, s = $13

Now,

we have to calculate percentage of homes will have a monthly utility bill of more than $79 i.e P(X > 79)

also,

P( X > 79) = 1 - P( X < 79)

Z-score for (X = 79 ) = $\frac{X-m}{s}$

Z = $\frac{79-92}{13}$

or

Z = -1

From the standard Z value vs P table, we have

P( Z < -1 ) = 0.1587

Thus,

P( X < 79) = P( Z < -1 ) = 0.1587

therefore,

P(X > 79) = 1 - 0.1587

or

P(X > 79) = 0.8413

or

= 0.8413 × 100%

= 84.13%

Hence,

option d) approximately 84%