the sample space of  population being researched contains 58 values and a mean of 318.6.The population has a known standard deviation of 29.2. Identify the margin of error for a 95% confidence interval estimate of the mean of the population.

ANSWER = 7.5150

I need the explanation and a step by step to better understnad why that is the answer. please help! I really want to understand this.
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1 Answer

With a sample size of this magnitude we can use 1.96 as the 95% confidence interval critical value from tables as the multiplier for the standard error, which is 29.2/√58=3.834 approx. The margin of error is therefore 1.96×3.834=7.5149. Therefore we have 318.6±7.515 as the error on the mean: 311.085<µ<326.115.

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