SOLUTION: a shoe manufacturing company is producing 50,000 pairs of shoes daily. from a sample of 500 pairs, 2% are found to be of substandard quality. at 95% level of confidence, estimate t
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Question 1205292: a shoe manufacturing company is producing 50,000 pairs of shoes daily. from a sample of 500 pairs, 2% are found to be of substandard quality. at 95% level of confidence, estimate the number of pairs of shoes that are reasonably expected to be spolied in the daily production. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! 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.
