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The time in hours for a worker to repair an electrical instrument is a Normally distributed...

The time in hours for a worker to repair an electrical instrument is a Normally distributed random variable with a mean of μ and a standard deviation of 50. The repair times for 12 such instruments chosen at random are as follows:

183 222 303 262 178 232 268 201 244 183 201 140

Part a) Find a 95% confidence interval for μ. For both sides of the bound, leave your answer with 1 decimal place. (  ,  ).

Part b) Find the least number of repair times needed to be sampled in order to reduce the width of the confidence interval to below 30 hours.

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