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Answer :
Final answer:
To find the minimal sample size needed to ensure that the sample mean length is within a certain range of the population mean, you need to use the formula: n = (Zσ/M)^2. 'Z' is the Z-score related to your desired confidence level, 'σ' is the population standard deviation, and 'M' is the margin of error. However, the specific margin of error desired is not provided in the question.
Explanation:
There seems to be some information missing in your question. Usually, we need to know the specific confidence interval or the margin of error (the missing interval you mentioned) to determine the sample size. However, the general formula for a sample size in this context is derived from the Central Limit Theorem. The formula is: n = (Zσ/M)^2.
Here, 'Z' is the Z-score derived from our desired level of confidence, 'σ' is the standard deviation (6.2 inches in this case), and 'M' is the margin of error. For example, if we needed to be within 1 inch of the population mean with 95% confidence, then 'Z' would be 1.96 (Z score for 95% confidence), 'M' would be 1.
We would plug in these values and solve the equation for 'n' (our required sample size). Please note that this method assumes a normal distribution of the population, as the question stated.
Learn more about Determining Sample Size here:
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