You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately
σ=39.7. You would like to be 95% confident that your estimate is within 3 of the true population mean. How large of a sample size is required?

Using the sample size relation with the standard normal distribution, the required sample size is 673 samples.

Substituting the values into the equation :

n = [(Z* × σ) / ME]²

n = [(1.96 × 39.7) / 3]²

n = (77.812 / 3)²

n = 25.937²

n = 672.7

Therefore, the Number of samples required is 673 samples.

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673 people

Step-by-step explanation:

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Use the margin of error formula.

ME = t*

3 = 1.96*

3/1.96 =

1.531 =

39.7/1.531 =

25.937 =

25.937^2 = ^2

672.7 = n

You need at least 673 people to be confident!