An engineer observes the assembly of 85 randomly selected steel support rods to
ID: 3152128 • Letter: A
Question
An engineer observes the assembly of 85 randomly selected steel support rods to determine the average time required for the different steps of the assembly process. It is discovered that it takes an average of 2.65 minutes to complete the final assembly step with a standard deviation of 0.250 minutes. Find the 90% confidence interval for the mean time required in the final assembly step. Find the 95% confidence interval for the mean time required in the final assembly step. Find the 99% confidence interval for the mean time required in the final assembly step. Determine how many rods will need to be sampled in order for a 95% confidence level specifies the mean assembly time of the final step to within Plusminus 10 seconds. What is the confidence level of the final assembly mean time interval (2.60 min, 2.70 min)?Explanation / Answer
Given that n = number of steel support rods = 85 Xbar = average = 2.65 sigma = 0.25 And we have to find 90% and 95% confidence interval for mean time required in the final assembly step.
Here we use confidence interval for Z because past data is given.
90% confidence interval :
c = 0.90
We can find confidence interval using TI-83 calculator.
Steps :
STAT --> TESTS --> 7:ZInterval --> ENTER --> Highlight on Stats --> ENTER --> Input values of sigma, Xbar, n and C-level --> Calculate --> ENTER
90% confidence interval for mean is (2.6054, 2.6946).
95% confidence interval :
By using TI-83 calculator steps 95% confidence interval for mean is (2.5969, 2.7031).