The following set of numbers form an ideal data set for the experiment of flipping a certain unfair coin, and counting the number of heads:

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2}

This question has 5 parts:

(a) Based on the numbers appearing in the ideal data set, how many flips must there have been in this experiment?

(b) Find the population mean of this ideal data set. Show enough work to make clear that you understand.

(c) Use the population mean to find the probability of heads on each individual flip. Show enough work to make clear that you understand.

(d)Find the population standard deviation. Work directly with the definition of standard deviation, and do not use any shortcut formulas. Show enough work to make clear that you understand.

(e)Now use the shortcut formula (involvingNandp) to compute the population standard deviation. You don't need to show work here.