Answer:
138
Step-by-step explanation:
Population standard deviation = [tex]\sigma = 120[/tex]
.95 probability of estimating the population mean monthly income within a margin of $20
So, Significance level = 1-0.95 = 0.05
α =0.05
Margin error = 20
[tex]ME =Z \times \frac{\sigma}{\sqrt{n}}[/tex]
Z at 0.05 = 1.96
[tex]20 =1.96 \times \frac{120}{\sqrt{n}}[/tex]
[tex]\sqrt{n} =1.96 \times \frac{120}{20}[/tex]
[tex]n =(1.96 \times \frac{120}{20})^2[/tex]
[tex]n =138.2976[/tex]
So, n = 138
Hence sample size should be 138 selected to obtain a .95 probability of estimating the population mean monthly income within a margin of $20
