An IQ test is designed so that the mean is 100 and the standard deviation is 21

Question

An IQ test is designed so that the mean is 100 and the standard deviation is 21 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 90% confidence that the sample mean is with 4 IQ points of the true mean. Assume that alpha = 21 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.)

Explanation / Answer

Here it is given that mean=100 and sd=21

Now as n is sufficient large and also it is given normal distribution we will consider z distribution

So Margin of error=z*sd/sqrt(n), here z=1.645 and E=4

Hence n=(z*sd/E)^2=75

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