A machine on an assembly line fills cans with quantities of food that are normally distributed with a standard deviation of 0.057 pounds. The mean quantity filled is estimated using a sample of 100 cans. What is the difference between the upper and lower limits of the 95% confidence interval for the mean?
A.0.0057 lb.
B.0.011 lb.
C.0.022 lb.
D.0.11 lb.
E.0.22 lb.
Since 95% of the samples will be within 2 sigma (standard deviations) of the mean, that range will be 0.114 lb wide.
The answer is D
To find the difference between the upper and lower limits of the 95% confidence interval for the mean, we need to calculate the margin of error and then multiply it by 2.
The margin of error can be found using the formula: Z * (standard deviation / square root of sample size)
Since the sample size is 100, the standard deviation is 0.057 pounds, and we want a 95% confidence interval, we need to find the value of Z for a 95% confidence level. For a normal distribution, the Z value is approximately 1.96.
Plug these values into the formula to calculate the margin of error: 1.96 * (0.057 / √100) = 1.96 * (0.057 / 10) = 0.01112 pounds.
The difference between the upper and lower limits of the 95% confidence interval is twice the margin of error, so: 2 * 0.01112 = 0.02224 pounds.
Therefore, the correct answer is C. 0.022 lb.