Question 866626
First find the sample mean. You do so by adding up all the numbers and dividing by 31 (since there are 31 numbers). 



Add up all the numbers to get 3281. Divide this by 31 to get 3281/31 = 105.8387



The sample mean is usually denoted xbar, so xbar = 105.8387 (this is approximate)


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Now we turn to this <a href="http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg">table</a>. Look in the row that starts with {{{infinity}}} and look above the 98%. The value you'll see in this spot is 2.326



The critical value is z = 2.326



This is the critical value for the 98% confidence interval.

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To sum things up, we found the following



xbar = 105.8387 (sample mean)
z = 2.326 (critical value for the 98% confidence interval)



values above are approximate



The values given to us were


n = 31 (sample size)
&#963; = 15 (population standard deviation)


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We can finally compute the lower bound L and the upper bound U of the confidence interval



L = xbar - z*&#963;/sqrt(n)
L = 105.8387 - 2.326*15/sqrt(31)
L = 99.57227
L = 99.57  <font color="blue">rounding to 2 decimal places</font>



U = xbar + z*&#963;/sqrt(n)
U = 105.8387 + 2.326*15/sqrt(31)
U = 112.1051
U = 112.11  <font color="blue">rounding to 2 decimal places</font>



The confidence interval [L,U] or (L,U) is approximately [99.57, 112.11] or (99.57, 112.11)



So the answer is <font color="red">99.57 to 112.11</font> which is <font color="red">choice D</font>