Answer: 48
Step-by-step explanation:
As per given , we have
Population standard deviation : [tex]\sigma=14\text{ millimeters}[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value for 95% confidence interval (refer to z-value table) = [tex]z_{\alpha/2}=1.96[/tex]
Margin of error : [tex]E=4\text{ millimeters}[/tex]
Formula , we use to find the sample size :
[tex]n=(\dfrac{z_{\alpha/2}\cdot\sigma}{E})^2\\\\ n=(\dfrac{1.96\cdot 14}{4})^2\\\\ n=(6.86)^2=47.0596\approx48[/tex]
Hence, the required sample size = 48
