Suppose that a person believes that his last year€™s weight was normally distributed with mean of 165 lb and standard deviation of 5 lb. That is, the prior pdf of μ is N(165, 25), or Ï€(μ) ~ N(165, 25). He expects his current weight X is normally distributed with mean m and standard deviation 7 lb. Following are 10 random measurements (in pounds) from this year.

Find a 95% credible interval for μ.

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176 165 180 172 175 179 166 177 184 183