SOLUTION: You measure 45 backpacks' weights, and find they have a mean weight of 49 ounces. Assume the population standard deviation is 14.8 ounces. Based on this, what is the maximal margin

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Question 1203901: You measure 45 backpacks' weights, and find they have a mean weight of 49 ounces. Assume the population standard deviation is 14.8 ounces. Based on this, what is the maximal margin of error associated with a 95% confidence interval for the true population mean backpack weight.
Give your answer as a decimal, to two places

ounces
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe this is how you would solve this.

population mean is 49
population standard deviation is 14.5
sample size is 45.

standard error is equal to standard devition divided by square root of sample size = 14.5/sqrt(45) = 2.16153.
z-score formula is z = (x-m)/s
z is the z-score
x is the samp[le mean
m is the population mean
s is the standard error.

95% confidence interval requires a z-score equal to plus or minus 1.95996.
that's a two tailed confience interval with 2.5% alpha on each end.
alpha is the area under the normal distribution curve that's not in the confidence interval.

using the z-score formula, you get:
on the high side z = (x-m/s becoms 1.95996 = (x-49)/2.16153.
solve for (x-49) to get (x-49) = 1.95996 * 2.16153 = 4.23651.
that's your margin of error.
solve for x to get high side raw score = 53.236517.

on the low side z = (x-m)/s becomes -1.95996 = (x-49)/2.16153.
solve for (x-49) to get (x-49) = -1.95996 * 2.16153 = -4.23651.
solve for x to get low side raw score = 44.76349.

round ansswers to two decimql places to get:
margin of error = 4.24
minimum value = 44.76.
maximum value = 53.34.

i used the calculator at https://davidmlane.com/hyperstat/z_table.html to confirm this answer is correct.
it is correct as long as you calculated the standard error correctly, which i think i did, and as long as my assumptions about what the problem is looking for is correct.

here's what the results from the calculator look like.