1. tickets are drawn at random with replacement from a box of numbered tickets. the sum of 25 draws has expected value equal to 50, and the SE is 10. If possible, find the expected value and SE for the sum of 100 draws. Or do you need more information?

2. One hundred draws are going to be made at random with replacement from the box [02346] True or false, explain

a) the expected value for the sum of the draws is 300.

b) the expected value for the sum of the draws is 300, give or take 20 or so.

c) the sum of the draws will be 300

d) the sum of the draws will be around 300, give or take 20 or so.

3.a) a coin is tossed 10,000 times. what is the chance that the number of heads will be in the range 4850 to 5150?

b) a coin is tossed 1000000 times. what is the chance that the number of heads will be in the range 498500 to 501500?

4. a coin is tossed 100 times

a) the difference "number of heads - number of tails " is like the sum of 100 draws from on of the following boxes. which one, and why?

i) [heads, tails]

ii) [-1 1]

iii) [-1 0]

iv) [0 1]

v) [-1 0 1]

b) find the expected value and standard error for the difference

5. a university has 30000 registered students. as part of a survey, 900 students are chosen at random. the average age of the sample students turns out to be 22.3 years, and the SD is 4.5 years.

a) the average age of all 30000 students is estimated as ___. this estimate is likely to be off by ___ or so.

b) find a 95% confidence interval for the average age of all 30000 registered students.