An IQ test is designed so that the mean is 100 and the standard deviation is 8 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 99​% confidence that the sample mean is within 2 IQ points of the true mean. Assume that σ=8 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.)

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An IQ test is designed so that the mean is 100 and the standard deviation is
8 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 99​% confidence that the sample mean is within 2 IQ points of the true mean. Assume that σ=8 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.)
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