SOLUTION: The amounts of electricity bills for all households in a particular city have an approximately normal distribution with a mean of $140 and a standard deviation of $30. Find the

Algebra ->  Probability-and-statistics -> SOLUTION: The amounts of electricity bills for all households in a particular city have an approximately normal distribution with a mean of $140 and a standard deviation of $30. Find the      Log On


   

Question 1186190: The amounts of electricity bills for all households in a particular city have an
approximately normal distribution with a mean of $140 and a standard deviation of
$30. Find the probability that the mean amount of electricity bills for a random sample
of 75 households selected from this city will be between $132 and $136. My email address is www.cosmashiltoon@gmail.com
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
population mean = 140.
population standard deviation = 30
sample size = 75

when you are dealing with the mean of a sample, you need to use the standard error.

standard error = standard deviation divided by square root of smaple size = 30 / sqrt(75) = 3.4641 rounded to 4 decimal places.

probability that the sample mean will be between 132 and 136 is is equal to .1136 = 11.36%.

calculator used can be found at https://davidmlane.com/hyperstat/z_table.html

here's a display of the results from using that calculator.