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PClab #4
There are 2 pop machines. 
One is a regular pop machine and it costs 75 cents for a pop.
The other is a RANDOM POP MACHINE painted in flashy colors and it plays 
wild, enticing music to attract attention. The random pop machine has 2 buttons
on its front marked "toss 2 coins - 2 heads gets you a free pop". When the 1st
button is punched the result of the toss is shown on a screen - heads or tails.
The 2nd button does the same. The chance of heads is 1/2 for each button. You 
put $1 in the random pop machine to play. You punch the two buttons and if you
get  2 heads your $1 is returned with your pop. Otherwise, you get your pop,
 but it keeps your $1.
(A moments thought shows that you get a free pop with chance 25% and a pop
 costs you $1 with chance 75%.)

(1) Use Minitab to simulate 500 attempts at the random pop machine (about a 
 semesters' worth of pop?). Use the session window commands:

MTB> random  500 C1 ;            # note this line ends in a semicolon
SUBC> binomial  1  .75 .          # note this line ends in a period

The resulting column C1 contains the costs (random) for 500 purchases. To get
the sum of this column, the total amount spent, use the command:

MTB> sum  C1

Repeat this 5 times and record your sums.

(2) Use our theory concerning random draws to figure out the expected value and 
    standard deviation for the sum of 500 such "draws". How did your 5 results
    in part (1) match the theory?

(3) The  following data gives the warp breakage during the weaving of fabric
    for a sample of yarns.

86	146	251	653	98	249	400	292	131	169
175	176	76	264	15	364	195	262	88	264
157	220	42	321	180	198	38	20	61	121
282	224	149	180	325	250	196	90	229	166
38	337	65	151	341	40	40	135	597	246
211	180	93	315	353	571	124	279	81	186
497	182	423	185	229	400	338	290	398	71
246	185	188	568	55	55	61	244	20	284
393	396	203	829	239	236	286	194	277	143
198	264	105	203	124	137	135	350	193	188

    Copy the data and paste it into the MINITAB spreadsheet in C1 to C10.
    To arrange these values into one column use the session command:
        Stack  c1-c10 c11
    Name column C11  "breakage".
    Give a dotplot of the data.
    Give a histogram of the data. 
    Further, try to experiment with the choice of intervals
    by using the session command like:
MTB> histogram  C1 ;
SUBC> cutpoints  0 50 100 150 500 .
    Choose your own values for the cutpoints - they specify the boundaries
    of the intervals you want to use.
    Produce a dotplot for the data.
    Get descriptive statistics for breakage.
    By hand, calculate a 95% confidence interval for the proportion of times
    the breakage exceeds 300 . (Count how many times this happens.)
    By hand, or with Minitab, calculate a 95% confidence interval for 
    the mean breakage of the underlying population.