Question

How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $140 of the population mean, and the population standard deviation is known to be $569.

Answer 1

Approximately 63 business students must be randomly selected to estimate the mean monthly earnings of business students at one college

Explanation:

confidence interval = 95%

Standard deviation
`(\sigma )` = 569

`\alpha` = 1 - 0.95 = .05

`Z_{(\alpha )/(2)}` =
`Z_{(.05 )/(2)}` = 1.96

We want 95% confidence that the sample mean is within $140 of the population mean

margin of error ( E ) =140

let n be the sample size

margin of error ( E ) =
`Z_{(\alpha )/(2)}(\sigma )/(√(n))`

squarring both side

`E^(2) = 1.96^(2)*(\sigma ^(2))/(n)`

`n = (1.96^(2))/(140^(2))* 569^(2)`

n = 63.45

n =63 approximately