# statistics

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Question 6: A manufacturer knows that the number of items produced per hour by its two factories A and B is normally distributed with standard deviations 8.0 and 11.0 items respectively. The mean hourly amount produced by Firm A from a random sample of 50 hours is 120 units and that by Firm B from a random sample of 30 hours is 110 units. Find the 95% confidence interval for the difference in the means and comment on the estimated interval.

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You will need to use a two-sample confidence interval formula.

Here is one example:

CI95 = (x1 − x2) ± z-value × √(s1^2/n1 + s2^2/n2)
(Note: × means to multiply)

x1 = mean A
x2 = mean B

z-value = 1.96

s1^2 = standard deviation A (squared)
s2^2 = standard deviation B (squared)

n1 = sample size A
n2 = sample size B

Plug the values into the formula and calculate the interval.

I hope this will help get you started.

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