Answer: (47.51, 54.49)
Step-by-step explanation:
Confidence interval for population mean is given by :-
![\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
, where n= sample size .
= population standard deviation.
= sample mean
= Two -tailed z-value for
(significance level)
As per given , we have
![\sigma=11.8\text{ ounces}](https://tex.z-dn.net/?f=%5Csigma%3D11.8%5Ctext%7B%20ounces%7D)
n= 44
Significance level for 95% confidence = ![\alpha=1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3D1-0.95%3D0.05)
Using z-value table ,
Two-tailed Critical z-value : ![z_{\alpha/2}=z_{0.025}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.025%7D%3D1.96)
Now, the 95% confidence interval for the true population mean textbook weight will be :-
![51\pm (1.96)\dfrac{11.8}{\sqrt{44}}\\\\=51\pm(1.96)(1.7789)\\\\=51\pm3.486644\approx51\pm3.49\\\\=(51-3.49,\ 51+3.49)\\\\=(47.51,\ 54.49)](https://tex.z-dn.net/?f=51%5Cpm%20%281.96%29%5Cdfrac%7B11.8%7D%7B%5Csqrt%7B44%7D%7D%5C%5C%5C%5C%3D51%5Cpm%281.96%29%281.7789%29%5C%5C%5C%5C%3D51%5Cpm3.486644%5Capprox51%5Cpm3.49%5C%5C%5C%5C%3D%2851-3.49%2C%5C%2051%2B3.49%29%5C%5C%5C%5C%3D%2847.51%2C%5C%2054.49%29%20)
Hence, the 95% confidence interval for the true population mean textbook weight. : (47.51, 54.49)