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please show all work!!!The lengths of adult males' hands are normally distributed with mean 195 mm...

please show all work!!!The lengths of adult males' hands are normally distributed with mean 195 mm and standard deviation is 7 mm. Suppose that 43 individuals are randomly chosen. Round all answers to 4 where possible.

  1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
  2. For the group of 43, find the probability that the average hand length is less than 194.
  3. Find the third quartile for the average adult male hand length for this sample size.
  4. For part b), is the assumption that the distribution is normal necessary? NoYes please show all work!

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