A recent survey of 50 fresh graduates revealed that it took an average of 3.5 weeks for them to secure a job position.The standard deviation for these fresh graduates to secure a job was 1.4 weeks

(a)Construct a 95% confidence interval for the population mean.

(b)How large a sample is needed to find the population mean within 0.2 weeks at 80% confidence interval?

(c)It was further known that the population mean is 4 weeks and population standard deviation is 2 weeks.What is the probability that the sample mean will be more than 3.8 weeks?