A certain adjustment to a machine will change the length of the parts it makes but will not affect the standard deviation. The length of the parts is normally distributed, and the standard deviation is 0.5 mm. After an adjustment is made, a random sample is taken to determine the mean length of parts now being produced. The resulting lengths are as follows.
| 75.4 |
75.9 |
75.3 |
77.4 |
75.8 |
76.6 |
76.8 |
75.2 |
76.8 |
77.4 |
(a) Find the point estimate for the mean length of all parts now being produced. (Give your answer correct to two decimal places.)
____________mm
(b) Find the 0.99 confidence interval for ?. (Give your answer correct to three decimal places.)