Answer: 41
Step-by-step explanation:
Given : Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Margin of error : [tex]E=4[/tex]
Standard deviation: [tex]\sigma=13[/tex]
The formula to find the sample size : [tex]n=(\dfrac{\sigma\times z_{\alpha/2}}{E})^2[/tex]
Then, we have
[tex]n=(\dfrac{13\times(1.96)}{4})^2=40.5769\approx41[/tex]
Hence, the minimum sample size needed= 41.
