The data below contain the number of defects observed on each of 50 lcd screens made by a certain manufacturer.

defects
1
4
2
3
1
0
4
3
1
1
6
3
4
0
5
2
1
2
0
2
2
1
4
2
2
2
3
2
3
3
5
4
2
1
2
4
2
2
2
3
3
2
2
2
2
2
1
3
4
1
construct a 95% confidence interval for the mean number of defects per screen for all screens produced by this manufacturer.
a) what is the lower limit on the interval? give your answer to three decimal places:

b) what is the upper limit on the interval? give your answer to three decimal places.

d) if we are very certain that the true standard deviation of the number of defects per screen is below 2, what sample size would be required so that the width of the 95% confidence interval for the mean number of defects per screen is at most 0.27? make sure you enter a whole number below.