Homework 6 Solutions

Ch. 16: 


4.  (a) 60 rolls.  With more rolls, the percentage of aces will be
closer to 16 2/3%.  You want the percentage of aces to be far from 16
2/3%.  Chance error in the percentages is working against you, so choose
the smaller number of rolls.

    (b) 600 rolls.  Now chance error in the percentages is working for
you, so choose the larger number of rolls.

    (c) 600 rolls.  Like (b).

    (d) 60 rolls.  As you roll more and more, there get to be more and
more possibilities; no particular one can be very likely.  Take a more
extreme case: with 6000 rolls you can get 1000 aces, or 1001, or 1002,
...  There are lots of possibilities, each one individually has a
small chance.



Ch. 17:


6.  observed value for the sum of the draws: 45(1) + 23(2) + 32(3) = 187
    observed value for the number of 3's: 32
    observed value for the number of 1's: 45
    expected value for the sum of the draws: [(1+1+2+3)/4][100] = 175
    expected value for the number of 3's: (1/4)(100) = 25
    expected value for the number of 1's: (2/4)(100) = 50
    chance error in the sum of the draws: 187 - 175 = 12
    standard error for the number of 1's: 10(1-0)[((1/2)(1/2))^0.5] = 5


11.  You have to change the box, so that it has 3 "0" tickets, 1 "1"
ticket, and 1 "3" ticket.  The average of the box is 0.8, and the SD
is about 1.2.  So the sum will be around 80, give or take 12 or so.



Ch. 18:


2.  (a) The average of the box is 4 and the SD is about 2.24; the
expected value for the sum is 1600 and the SE is about (400)^0.5 x
2.24 (about 45).  The chance is about 99%.

    (b) The number of "3"'s is like the sum of 400 draws from a box
with 3 "0" tickets and 1 "1" ticket.  The expected number is 100 and
the SE is 8.66.  The chance is about 12%.  (If more accuracy is
desired, use the continuity correction.)


6.  No, the COIN program did not pass.  The expected number of heads
is 500,000.  The standard error for the total number of heads is 500.
So having 2,015 more heads than expected is more than 4 SE's away from
what was expected.  It is possible to get this many heads with a fair
coin, but it is extrememly unlikely.  The program should be retested,
and if it continues in this way, we will know that it is not
performing properly.