A simple random sample of the weights of 40 women has mean of 146.22 lb. Reasearch from other sources suggests that the population standard deviation of weight of women is 30.86lb. Find a 95% confidence interval estimate of the mean weight of all women. 

I know the answer is 136.66 lb<u<155.78lb but I just need a step by step explaination on why this is the answer! I'd be greatly appreciated <3 

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In this case we need to work out the standard error first=30.86/√40=4.88 approx. Next we find the 2-tailed critical value for 95% (where significance level ɑ=1-0.95=0.05) and from normal distribution tables this corresponds to 1.96 standard deviations. We multiply 4.88 by this critical value=9.564 approx. This gives us the margin on either side of the mean: 146.22±9.56: 136.66<µ<155.78.

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