Question

Electricity consumption by the residents in a local community is normally distributed, with a mean of 32 kilowatt-hours per day. Ninety-five percent of the residents use between 28 and 36 kilowatt-hours per day. What is the standard deviation of electricty consumption in the population?

Answer 1

Answer:

The standard deviation is 2

Step-by-step explanation:

Electricity consumption by the residents in a local community is normally distributed, with a mean of 32 kilowatt-hours per day.

We have that, 95% of the residents use between 28 and 36 kilowatt-hours per day.

According to the empirical rule , 95% of the distribution falls within two standard deviations of the mean.

We can use the upper x=36, and the mean,

$\mu = 32$

to find the standard deviation using the formula:

$\frac{x - \mu}{ \sigma} = z$

We substitute to get:

$\frac{36- 32}{ \sigma} = 2$

$\frac{4}{ \sigma} = 2 \\ \frac{4}{ 2} = \sigma \\ \sigma = 2$

Therefore the standard deviation is 2.