Hannibal wants to estimate the true average brain mass, u, but he is locked in a cell with no internet and only has a scale. He collects a small random sample of size n = 5 from nearby prison guards. He find that these brains have the following weights:
1320g, 1400g, 1300g, 1460g, 1350g

Suppose that human brains follow a normal distribution, and that Hannibal's sample is representative of the entire population.

a. (1 pt) Compute the sample standard deviation, s, of these brains. Do not use a computer for part (a). You may only use +, -, X, -, and ✓ on a calculator. Show all your work.
b. (1 pt) Construct a two-sided 95% confidence interval for the true mean weight of brains, u. You may use a computer/calculator to calculate critical values, but not to solve the entire problem.
c. (1 pt) Construct a two-sided 82% confidence interval for the true mean weight of brains, u.
d. (1 pt) Construct a one-sided 95% confidence interval for the true mean weight of brains, u. Give the lower bound. Your interval will look like this: (Lower Bound, 00)