A normally distributed population has mean 57.7 and standard deviation 12.1Find the probability that the mean of a sample of size 16 drawn from this population is less than 45

The question:This project is split into two tasks.Task 1: Show all necessary workings (use Excel) and convert it to word. Include graphs as well (hypothesis graphs) Prepare a report in MS Word. The top food snacks consumed by adults aged 18 – 54 are gum, chocolate candy, fresh fruit, potato chips, breath mints/ candy, ice-cream, nuts, cookies, bars, yogurt, and crackers. Select random samples of people from two different age groups (18 – 21 and 21 & above) and find the respective proportions who ranked fruit fresh as their top snack choice (surveys are required, but numbers can be made up)a) Is there a difference in the proportion of different age groups who rank fresh fruit as their top snack? Test at two appropriate significance levels and comment on your findings. Specify the test statistic you use and its distribution under the null hypothesis.b) Construct a 95% confidence interval for the difference in the proportions.Task 2: No actual calculations are required. Prepare summary in MS Word.You work for a market research company and your boss has asked you to carry out a random sample survey for a mobile phone company to identify whether a recently launched mobile phone is attractive to younger people. Limited time and money resources are available at your disposal.You are being asked to prepare a brief summary.

calculus help on May 17 UK time 3 pm (It might be shifted to 18th. Most probably, it won't)You will have 4 hours to finish this as the teacher gives that much time so we can finish anytime but you can see the sample and you can see it will take 1 hour or so if you know the topics. Topics are:Limits , Riemann integral , Improper integrals,Double integrals ,Manipulation of integrals ,An introduction to theLebesgue integral , Laplace transforms