Answer:
99% Confidence Interval = (5.824,6.036)
Explanation:
The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup. Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of .13 ounces. Construct a 99 percent confidence interval for the true machine-fill amount.
The formula for confidence interval
= Mean ± z × σ/√n
Mean of 5.93 ounces
Standard deviation of .13 ounces.
n = 10 cups
z= z score of 99% confidence interval = 2.58
Confidence Interval =
5.93 ± 2.58 × 0.13/√10
5.93 ± 2.58 × 0.0411096096
Confidence Interval = 5.93 ± 0.106
= 5.93 - 0.106
= 5.824
= 5.93 + 0.106
= 6.036
Hence, Confidence Interval = (5.824,6.036)