The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes and is normally distributed.

a) After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 92% confidence interval for the mean assembly time.

b) How many workers should be involved in this study in order to have the mean assembly time estimated up to

a. Mean assembly time is estimated to fall between 15.6mins and 16.8mins with a 92% CI.

b.636 workers

Step-by-step explanation:

Let denote the mean assembly time in minutes.

Standard deviation,

To obtain a 92%CI for based on given parameters:,. is known, therefore we use the interval:

Where, and is obtained from the z-interval tables.

b. A sample of size n needs to be completed based on the info:, E denotes the margin of error.

Therefore the sample size is calculated as:-

Hence, 636 workers should be involved in this study in order to have the mean assembly time required.

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