A) if a sample of 51 light bulbs has an average life of 2050 hours with sample standard deviation of 58 hours, find a 95% confidence interval for the population mean of all light bulbs produced by this firm using LARGE SAMPLE INTERVALB) now suppose we guess the population standard deviation as 60 hours and we have not collected a sample yet. How large of a sample is needed if we wish to be 95% confident and that our sample mean will b within 10 hours of the true mean? (Hint: that is to keep the half interval length to be within 10, in other words we do not multiply 4 in the formula)*Please so part A and part B, thank you

3. (15 Points Total) An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed. a. (8 Points) If a sample of 51 light bulbs has an average life of 2050 hours with sample standard deviation of 58 hours, find a 95% confidence interval for the population mean of all light bulbs produced by this firm using large sample interval. b. (7 Points) Now suppose we guesstimate the population standard deviation as 60 hours and we have not collected a sample yet. How large a sample is needed if we wish to be 95% confident that our sample mean will be within 10 hours of the true mean? (Hint: That is to keep the half-interval length to be within 10 in other words, we do NOT multiply 4 in the formula)