PV Gap

Felicia Said:

Statistics Studying Need Comprehensive Solution Q.4?

We Answered:

Greetings,

You have been given a mean and standard deviation of a symmetric mound-shaped distribution. This means a normal distribution.

So calculate a z-score for 85 and find the area of the normal curve to the right of this. The area of the normal distribution to the right of the point corresponding to 85 will be the percentage of homes with a bill of more than 85.

z = (85 - 97)/12 = -1

From your z-score table the area from -1 to 0 is 34.13% and the area from 0 to inf is 50% so the total percentage is 84%

Regards

Louise Said:

Statistics Question Requires C. Rule?

We Answered:

For this you will need Chebyshev's inequality. It states that for any random variable X having finite mean ? and standard deviation ? and any real number k>0:

P(|X - ?| ? k?) ? 1/k².

In this case, letting X be the monthly utility bill, we see that it has mean 126 and standard deviation 14. If X was less than 98, then |X-126| ? 28 = 2*14, so we see that:

P(X<98) ? P(|X-126| ? 2*14) ? 1/2² = 1/4

So at most 1/4 of the homes will have a monthly utility bill less than $98.