Answer:
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
