The cycle times for an electroplating machine are believed to be normally distributed.Twenty-one plating operations are randomly sampled, and cycle times are recorded.The sample average cycle time is 10.21 min, with a standard deviation of 0.59 min.What is a 95% confidence interval for the mean cycle time on this machine?
A) (9.958, 10.462)
B) (9.941, 10.479)
C) (8.979, 11.441)
D) (9.911, 10.509)

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval for the population mean:

CI = X̄ ± tα/2 * (s/√n)

Where X̄ is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the critical t-value from the t-distribution with degrees of freedom n-1 and α level of significance. For a 95% confidence interval, α = 0.05/2 = 0.025 and degrees of freedom = 20.

Substituting the given values, we get:

CI = 10.21 ± 2.093 * (0.59/√21)

CI = (9.941, 10.479)

Therefore, the best choice is B with the explanation provided above.

The Cycle Times for an Electroplating Machine Are Believed to Be