The amount of weight a high school student carries in his or her bookbag follows a normal distribution with a standard deviation of σ = 2 pounds. Suppose a random sample of 20 bookbags produced a mean of 13 pounds. Construct a 95% confidence interval to estimate the mean bookbag weight for all high school students.

Given Data :

Sample mean $(x\bar)=13$

Population standard deviation $(\sigma) = 2$

Sample size $(n) = 20$

Confidence interval level $(CI) =95%$

The level of significance:

$$\alpha=1-0.95=0.05$$

The critical value:

$$z_c=Z_\frac\alpha2=Z_\frac{0.05}2=1.96$$

The confidence interval:

$$CI = \overline{x} \pm z_c \cdot \frac{\sigma}{\sqrt{n}} = 13 \pm 1.96 \cdot \frac{2}{\sqrt{20}} = (12.118, 13.882)$$