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,
[tex] \mu = 32[/tex]
to find the standard deviation using the formula:
[tex] \frac{x - \mu}{ \sigma} = z[/tex]
We substitute to get:
[tex]\frac{36- 32}{ \sigma} = 2[/tex]
[tex]\frac{4}{ \sigma} = 2 \\ \frac{4}{ 2} = \sigma \\ \sigma = 2[/tex]
Therefore the standard deviation is 2.
