6 assemblies were found to have an average weight of 9.2 ounces with a sample standard deviation is 0.7. Find the 95% confidence interval of the true mean weight

8.6 < µ < 9.8                                

Step-by-step explanation:

Solution:

The general formula for a confidence interval around a population mean (µ) is:

                                   Xbar ± Zα/2[S/√N]  

- Where Xbar is the mean of your sample (= 9.2)

- S is the sample standard deviation (= 0.7)

- N is the number of samples ( = 6)

- Assuming sample size is large enough.

- Z_α/2 is the Z-value in the standard normal table. In this case Z_α/2 = 1.96. (95% confidence interval)

- So your 95% confidence interval is:

                                 µ =Xbar ± Zα/2[S/√N]  

                                 µ = 9.2 ± 1.96[0.7/√6]    

                                 µ = 9.2 ± 0.5601166545  

                            µ is approximately 8.64 or 9.76

- The 95% confidence interval of the true mean weight lies between 8.6 < µ < 9.8