Question 1196689
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Given info:
n = 50 = sample size
xbar = 5.11 = sample mean
sigma = 0.1 = population standard deviation


Side note: In many real world situations, we often won't know what sigma is because it's a population parameter. The goal of statistics is to estimate such parameters. 


At 95% confidence, the z critical value is roughly z = 1.96
Use a table like this
<a href = "https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a>
to get that value. Look at the bottom row labeled "Z" and above the 95% confidence level.


Use those values to find the following.
E = margin of error
E = z*sigma/sqrt(n)
E = 1.96*0.1/sqrt(50)
E = 0.02771858582251
E = 0.027719
The result is approximate


The value of E is the distance from the center to either endpoint. 
Think of it as the radius of interval.
It's half the confidence interval width, so the full width is 2*E = 2*0.027719 = 0.055438


You could also follow these steps
L = lower bound
L = xbar - E
L = 5.11 - 0.027719
L = 5.082281
U = upper bound
U = xbar + E
U = 5.11 + 0.027719
U = 5.137719
The width of the confidence interval is U - L = 5.137719 - 5.082281 = 0.055438 which is the distance from the lower bound L to the upper bound U.
These steps are handy if you are given the confidence interval in the format (L,U) or the format L < mu < U.
Note how U - L = (xbar+E)-(xbar-E) = 2E, so the xbars cancel out and the E's double up.



Answer: 0.055438 approximately
Round that value however needed.
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