## The cycle times for an electroplating machine are believed to be normally distributed. Twenty-one plating operations are randomly sampled fo

Question

The cycle times for an electroplating machine are believed to be normally distributed. Twenty-one plating operations are randomly sampled for time to cycle. The sample average cycle time is 10.21 minutes with a standard deviation of 0.59 minutes. Construct a 95% confidence interval on the mean cycle time for this machine.

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2022-01-01T14:20:44+00:00
2022-01-01T14:20:44+00:00 1 Answer
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## Answers ( )

Answer:The 95% confidence interval on the mean cycle time for this machine is between 8.98 minutes and 11.44 minutes.

Step-by-step explanation:We are in posession of the sample’s standard deviation, so we use the students’ t-distribution to solve this question.

The

first stepto solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. Sodf = 21 – 1 = 20

95% confidence intervalNow, we have to find a value of T, which is found looking at the t table, with 20 degrees of freedom(y-axis) and a confidence level of ). So we have T = 2.086

The margin of error is:M = T*s = 2.086*0.59 = 2.13

In which s is the standard deviation of the sample.

The

lower endof the interval is the sample mean subtracted by M. So it is 10.21 – 1.23 = 8.98 minutesThe

upper endof the interval is the sample mean added to M. So it is 10.21 + 1.23 = 11.44 minutesThe 95% confidence interval on the mean cycle time for this machine is between 8.98 minutes and 11.44 minutes.