Question 1205292
production is 50,000 pairs of shoes daily.
sample size is 500.
2% of the 500 were found to be of substandard quality.
.02 * 500 = 10.
10 out of the 500 were found to be defective.
the mean is 10.
the standard deviation is sqrt(n * p * q) = sqrt(500 * .02 * .98) = 3.130495.


critical z-score at 95% two tail confidence interval is equal to plus or minus 1.96.


on the low end of the confidence interval, the formula becomes -1.96 = (x - 10) / 3.120495.
solve for x to get x = 3.86423.


on the high end of the confidence interval, the formula becomes 1.96 * (x - 10) / 3.120495.
solve for x to get x = 16.13577.


your 95% confidence interval is from 3.86423 to 16.13577.


here's what it looks like on a normal distribution graph.


<img src = "http://theo.x10hosting.com/2023/120702.jpg">