Answer:
Approximately 63 business students must be randomly selected to estimate the mean monthly earnings of business students at one college
Step-by-step explanation:
confidence interval = 95%
Standard deviation [tex](\sigma )[/tex] = 569
[tex]\alpha[/tex] = 1 - 0.95 = .05
[tex]Z_{\frac{\alpha }{2}}[/tex] = [tex]Z_{\frac{.05 }{2}}[/tex] = 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 ) = [tex]Z_{\frac{\alpha }{2}}\frac{\sigma }{\sqrt{n}}[/tex]
squarring both side
[tex]E^{2} = 1.96^{2}\times\frac{\sigma ^{2}}{n}[/tex]
[tex]n = \frac{1.96^{2}}{140^{2}}\times 569^{2}[/tex]
n = 63.45
n =63 approximately
