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The average price of an item is $42 with a standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation!

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francocanacari

The mean price goes between $ 41.16 and $ 42.84, so a value of $ 48 is unusually high.

Since the average price of an item is $ 42 with a standard deviation of $ 3, to find a 98% confidence interval about the mean, and determine if a value of X = 48 is unusually high or if it is normal, the following calculations should be done:

  • (((42 - 3) + (42 + 3)) / 2) x 0.98 = X
  • ((39 + 45) / 2) x 0.98 = X
  • 42 x 0.98 = X
  • 41.16 = X

  • (((42 - 3) + (42 + 3)) / 2) x 1.02 = X
  • ((39 + 45) / 2) x 1.02 = X
  • 42 x 1.02 = X
  • 42.84 = X

Therefore, as the mean price goes between $ 41.16 and $ 42.84, a value of $ 48 is unusually high.

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