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](https://tex.z-dn.net/?f=%20%5Cmu%20%3D%2032)
to find the standard deviation using the formula:
![\frac{x - \mu}{ \sigma} = z](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20-%20%20%5Cmu%7D%7B%20%5Csigma%7D%20%20%3D%20z)
We substitute to get:
![\frac{36- 32}{ \sigma} = 2](https://tex.z-dn.net/?f=%5Cfrac%7B36-%20%2032%7D%7B%20%5Csigma%7D%20%20%3D%202)
![\frac{4}{ \sigma} = 2 \\ \frac{4}{ 2} = \sigma \\ \sigma = 2](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B%20%5Csigma%7D%20%20%3D%202%20%5C%5C%20%5Cfrac%7B4%7D%7B%202%7D%20%20%3D%20%5Csigma%20%5C%5C%20%5Csigma%20%3D%202)
Therefore the standard deviation is 2.
The answer is A) (3.1, 2.2)
Step-by-step explanation:
-4 x 0.3 = -1.2
f(0.3) = -1.2 -6
-1.2 - 6 = -7.2
f(0.3) = -7.2