The time in hours for a worker to repair an electrical instrument is a Normally distributed random variable with a mean of ? 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 ?. 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 26 hours.