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An IQ test is designed so that the mean is 100 and the standard deviation is 12 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with

`95%`

confidence that the sample mean is within 7 IQ points of the true mean. Assume that

`\sigma =12`

and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. The required sample size is

`?`

(Round up to the nearest integer.) Would it be reasonable to sample this number of students? Yes. This number of IQ test scores is a fairly small number. No. This number of IQ test scores is a fairly small number. Yes. This number of IQ test scores is a fairly large number. No. This number of IQ test scores is a fairly large number.