SOLUTION: Find each probability a. P(5;4) b. P(2;4) c. P(6;3) d. P(10;7) e. P(9;8) Part 2 A copy machine randomly puts out 10 blank sheets per 500 copies processed. Fi

Algebra ->  Probability-and-statistics -> SOLUTION: Find each probability a. P(5;4) b. P(2;4) c. P(6;3) d. P(10;7) e. P(9;8) Part 2 A copy machine randomly puts out 10 blank sheets per 500 copies processed. Fi      Log On


   

Question 694369: Find each probability
a. P(5;4)
b. P(2;4)
c. P(6;3)
d. P(10;7)
e. P(9;8)

Part 2
A copy machine randomly puts out 10 blank sheets per 500 copies processed. Find the probability that in a run of 300 copies, 5 sheets of paper will be blank.
Part 3
A recent study of robberies for a certain geographic region showed an average of 1 robbery per 20,000 people. In a city of 80,000 people, find the probability of the following:
a. 0 robberies
b. 1 robbery
c. 2 robberies
d. 3 or more robberies

part 4.
In a 400 page manuscript, there are 200 randomly distributed misprints. If a page is selected, find the probability that it has 1 misprint.
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
1.
Probability of event A that occurs:
P%28A%29+=+n%28A%29+%2F+n%28S%29
P%28A%29+=+4+%2F+5
P%28A%29+=+highlight%280.8%29
Probability of event A that does not occur:
P(A') = 1+-+P%28A%29
P(A') = 1+-++0.8
P(A')= 0.2

2.
A copy machine randomly puts out 10 blank sheets per 500 copies processed.
p=10%2F500=highlight%280.02%29
the probability that in a run of 300+copies, 5+sheets of paper will be blank is
p=5%2F300=0.016666666666666666666666666666667 ≈ highlight%28p=0.017%29
3.
Prob%28+a+robbery%29+=+20000%2F80000=1%2F4+=+0.25
n=80000
The Binomial distribution has the probability
function P%28x=r%29=+nCr+p%5Er+%281-p%29%5E%28n-r%29
r=0,1,2,.....,n
where nCr+=+n%21+%2F+%28r%21+%28n-r%29%21%29
For 80000 people, we expect 4 robberies.
a)
n=80000
p=4%2F80000
p=1%2F20000
highlight%28r=0.00005%29


use the source to compute
%2880000C0%29%281%2F20000%29%5E0%2819999%2F20000%29%5E8000=+0.018
Using Poisson with lambda+=4
P%28x=0%29=+e%5E-4+%2A%284%5E0+%2F+1%21%29=0.018%281%2F1%29=highlight%280.018%29

b)

highlight%28r=1%29
Using Poisson with lambda=4
e%5E-4%284%5E1+%2F+1%21%29=0.018%2A4=highlight%280.072%29

c)
highlight%28r=3%29


d)
p( highlight(x >=3))= p( 3 through 20000)
np=80000%280.00005%29=4
variance=np%281-p%29=3.99998
sd=1.99999
P%28+x+%3E=3%29+=+P%28+z+%3E%283-4%29%2F2%29+=+p%28+z+%3E+-0.5%29=highlight%280.6915%29
This uses normal approximation instead of Binomial because n is too large and p is too small.
4.
Presuming there are 200 of 400 total pages with misprints, there is a 50% probability of discovering one on any given page.
p=200%2F400=1%2F2=0.50 which is highlight%2850%29%