The 99% confidence interval will be (71.76, 78.23), (55.27, 56.73), and (38.71, 41.29).
The test statistic for 99% confidence interval is 2.58. Therefore, the 99% confidence interval when x = 75, s = 10, and n =64 will be:
= [75 - (10 × 2.58)/✓64, 75 + (10 × 2.58)/✓64,]
= 71.76, 78.23
The 99% confidence interval when x = 56,5 = 2, and n= 50 will be:
= [56 - (2 × 2.58/✓50), 56 + (2 × 2.58/✓50)]
= 55.27, 56.73
The 99% confidence interval when x = 40, s = 3, and n = 36 will be:
= [40 - (3 × 2.58)/✓36, 40 + (3 × 2.58)/✓36]
= 38.71, 41.29
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