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

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 $(\sigma )$  = 569

$\alpha$ = 1 - 0.95 = .05

$Z_{\frac{\alpha }{2}}$  = $Z_{\frac{.05 }{2}}$  = 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 ) = $Z_{\frac{\alpha }{2}}\frac{\sigma }{\sqrt{n}}$

      squarring both side

$E^{2} = 1.96^{2}\times\frac{\sigma ^{2}}{n}$

$n = \frac{1.96^{2}}{140^{2}}\times 569^{2}$

n = 63.45

n =63 approximately