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 $135 of the population mean, and the population standard deviation is known to be $538.

Answer 1

Answer: There are 61 business students must be randomly selected to estimate the mean monthly earnings of business students at one college.

Step-by-step explanation:

Since we have given that

mean = $135

Standard deviation = $538

At 95% level of confidence, z = 1.96

So, we get that

$\bar{x}=z\dfrac{\sigma}{\sqrt{n}}\\135=1.96\times \dfrac{538}{\sqrt{n}}\\\\\dfrac{135}{1.96}=\dfrac{538}{\sqrt{n}}\\\\68.87=\dfrac{538}{\sqrt{n}}\\\\\sqrt{n}=\dfrac{538}{68.87}\\\\\sqrt{n}=7.8\\\\n=7.8^2\approx 61$

Hence, there are 61 business students must be randomly selected to estimate the mean monthly earnings of business students at one college.