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12 March, 15:44

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

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  1. 12 March, 16:06
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    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
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