1: A fair coin is tossed 80 times. Find the probability for the following outcomes:

1. The number of heads equal to the number of tails.
2. The number of heads is between 45 and 52 (but does not include).
3. The number of heads is between 45 and 52 (inclusive).

2: 12 individuals are chosen at random from a normal population whose variance is 15 and their weights are as follows:

60.2, 58.4, 65.6, 62.8, 62.1, 63.5, 66.3, 65.0, 59.8, 68.5, 70.0, and 72.3

Construct 99% confidence interval for the mean weight of population.

Draw all possible samples of size 3 without replacement from the population. 0, 4, 13, 20, 27, 30 Show that a. Mean of X = # b. v(x) = " N-H N-1