71.4k views
3 votes
Suppose the heights of seasonal pine saplings are normally distributed. If the population standard deviation is 14 millimeters, what minimum sample size is needed to be 95% confidence that the sample mean is within 4 millimeters of the true population mean?​

User Suhas
by
7.3k points

1 Answer

3 votes

Answer: 48

Explanation:

As per given , we have

Population standard deviation :
\sigma=14\text{ millimeters}

Significance level :
\alpha=1-0.95=0.05

Critical value for 95% confidence interval (refer to z-value table) =
z_(\alpha/2)=1.96

Margin of error :
E=4\text{ millimeters}

Formula , we use to find the sample size :


n=((z_(\alpha/2)\cdot\sigma)/(E))^2\\\\ n=((1.96\cdot 14)/(4))^2\\\\ n=(6.86)^2=47.0596\approx48

Hence, the required sample size = 48

User Dino Babu
by
6.9k points