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Question 403:



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The sample size of 54 is reasonably large that we can use the normal, instead of t-distribution to compute the confidence interval. We'd also need to assume the interval is symmetrical around the mean and the information given here does not suggest otherwise. We need to work backwards from an already calculated interval.

The confidence interval is equal to the Margin of Error times a critical value based on the Confidence Level. In this case that level is 98%. To find the critical value we'd lookup the z-score for 98 percent of the area under the normal curve using the percentile to z-score calculator.

  1. The width of the CI is twice the Margin of Error, therefore the Margin of Error is (87.78-67.4)/2 = 10.19
  2. The Margin of Error is composed of the Standard Error of the Mean times the critical value.
  3. The critical value for a 2-sided 98% CI is 2.33.
  4. The Margin of Error is made up of the standard deviation divided by the square root of the sample size.
  5. We setup an equation and solve for the unknown standard deviation--the rest we know.
    1.  ( s/SQRT(54) ) * 2.33 = 10.19
    2.  s/SQRT(54) = 10.19/2.33
    3. s/SQRT(54) = 4.37
    4. s/7.35  = 4.37
    5. s = 32.12

So your standard deviation is around 32.12 million

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