Posted by **Bunny** on Saturday, May 5, 2012 at 9:29am.

The average electric bill in a residential area is $72 for the month of May. The standard deviation is $6. If the amounts of electric bills are normally distributed, find the probability that the mean of the bill for 15 residents will be less thatn $75

- statistics -
**David Q/R**, Saturday, May 5, 2012 at 2:22pm
You need to work out the standard deviation of the mean of the bill for 15 residents. That's $6//sqrt(15), which is 1.549. So the distribution of the mean of the bill for 15 residents will be Normal, with mean $72 and standard deviation 1.549. You have to work out the probability that the mean will be less than $75, so you need work out how many standard deviations $75 is above $72, which is ($75 - $72) divided by $1.549, which is 1.936. You now need to know what the area to the left of that point (because you want the probability of the mean bill being less that $75) is, and you can get that from a set of Normal probability tables. If you were looking up 1.96 you would get an answer of 0.975, so you know it's going to be a bit less than that. I've just looked it up myself, and I get 0.9735 - so I reckon that's your answer - i.e. just over 97%.

## Answer This Question

## Related Questions

- statistics - The customer bills in a family restaurant are normally distributed...
- Statistics - Electricity bills in a certain city have mean $120.08. Assume the ...
- Statistics - The amount of Jen's monthly phone bill is normally distributed with...
- statistics - The diameter of an electric cable is normally distributed, with a ...
- statistics - The diameter of an electric cable is normally distributed, with a ...
- Statistics - The diameter of an electric cable is normally distributed, with a ...
- statistics - The diameter of an electric cable is normally distributed, with a ...
- algebra - Diameter of an electric cable is normally distributed with a mean f 0....
- Statistics - The amount of a monthly phone bill is normally distributed with a ...
- Statistics - Electricity bills in a certain city have mean $108.73. Assume the ...

More Related Questions