An electrical power company is looking to expand into a new market. Before they commit to supplying the new area with electricity, they would like know the mean daily power usage for homes there. However, measuring the daily power usage of every home is not practical. Thus, an experiment must be designed where a sample of homes will have their daily power usage measured. Determine the required sample size to ensure that the 95% confidence interval for the population mean daily power usage is not larger than ±5 kWh. That is, determine the minimum sample size such that the error between the sample mean �" and population mean µ does not exceed 5 kWh, with 95% confidence. Based on historical trends, the population standard deviation can safely be assumed to be 50 kWh.

Given that an electrical power company is looking to expand into a new market. Before they commit to supplying the new area with electricity, they would like know the mean daily power usage for homes there.

Population std deviation = [tex]\sigma = 50[/tex]

Sample size =[tex]n[/tex]

STd error of sample mean = [tex]\frac{50}{\sqrt{n} }[/tex]

Margin of error for 95% would be Critical value ( std error)

Here since population std dev is known we can use Z critical value= 1.96

[tex]1.96*\frac{50}{\sqrt{n} }<5\\n>19.6^2\\n>384.16[/tex]

Sample size should be atleast 385