Vinod Banerjee owns a tea estate in Darjeeling.The tea leaves are collected every day and supplied to the tea factory located nearby.The tea factory operates a 25-day cycle for making payments to the suppliers of the tea leaves.The payment to the suppliers is based on the "turn-out" percentage.The turn-out percentage is nothing but the ratio of made tea by weight to the green tea leaves by weight, expressed as a percentage.For example, if 100 kgs of green tea leaves is processed and 7.2 kgs of made tea is produced, then the turn-out is 7.2%.The ideal turn-out is 8%.A high turn-out indicates low quality (the turn-out is high because the green tea leaves contain more mature leaves and stems), while a low turn-out is not desirable because it effects the revenues of the factory.In a 25-day cycle, the factory calculates the average turn-out for the 25 days (you can consider this as a sample of 25 observations) and makes the payment based on the average turn-out percentage.Vinod Banerjee knows that the population standard deviation () is 3.4%.

1.The factory manager calculated a 95% confidence interval for the long-term average turn-out of Vinod's tea estate based on the 25 day cycle.The tea factory has decided to reduce the payment cycle to 16 days (in order to improve the working capital situation of its suppliers).If the factory manager wants to retain the width of the new confidence interval based on 16 day-cycle same as that of the earlier interval (that was based on 25-day cycle), what will be the confidence level of the new interval?

A.88%$

B.12%

C.94%

D.6%

2.Banerjee is happy with the 16 day cycle but not comfortable with the change in the width of the confidence interval.He knows that he can control the variance of the turn-out by picking the right type of tea leaves.What should be the value of new variance of the turn-out, if he desires the same width of the original interval with 25 day cycle and 95% confidence level, but with a sample size of 16 (i.e., 16 day cycle)?

A.0.68

B.4.624

C.2.72

D.7.40$