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619snake
08-13-2010, 02:07 PM
1. The problem statement, all variables and given/known data
the weight of items produced by a production line is normally distributed with a mean of 12 ounces and a standard deviation of 2 ounces.
a. what is the probability that a randomly selected item will weight between 8 and 16 ounces? (DONE)
b. what is the probability that a randomly selected item will weight over 20 ounces? (DONE)
c. Suppose that quality control requires the weight of items to be within 8 and 16 ounces. You select 7 items at random (each item is independent). What is the probability that 3 of the items will fulfill quality control requirements. (DONE BUT HAVE DOUBTS)
d. find the probability that a randomly selected item has a weight that is greater than 14 or smaller than 10. (STUCK IN THIS ONE)

2. Related formulas
if x is BIN
p(x=k) = (n!)/((n-k)!(k!)) *(pi)^k * (1-pi)^(n-k)
mean = n(pi)
variance = n(pi)(1-(pi))

if x is N(&#181;,σ), then z=(x-&#181;)/(σ) is N(0,1)

3. The attempt at a solution
a. x~n (&#181;=12, σ=2)
p(8<x<16)
p(x<16) - p(x<8)
z=(16-12)/2 z=(8-12)/2
z=2 z= -2
p(z<2)-p(z<-2)
=.9772-.0228
=.9544

b.P(x>20)
z=(20-12)/2
z=4
p(z>4)= 1

c.x~binomial (&#181;=7, =.95)
p(x=3)
p(x=K)= (3!)/((3!)(7-3)!)*(.95)^3 *(1-.95)^4
.
.
.
x=0.000187551

d. I have no idea how to deal with this one
I think I have to use the mean and standard deviation of the problem
(&#181;=12, =2)
P(x<10) or P(x>14)
Hope you people can help me

Dason
08-13-2010, 02:21 PM
[B]c.x~binomial (µ=7, =.95)
p(x=3)
p(x=K)=(.95)^3 (1-.95)^4
.
.
.
x=0.000187551

You're final solution looks correct to me but you forgot the 7!/(3!4!) constant out front when you were deriving the answer.

d. I have no idea how to deal with this one
I think I have to use the mean and standard deviation of the problem
(µ=12, =2)
P(x<10) or P(x>14)
Hope you people can help me
An easier way to do problems like these is to find the probability of getting the complement of what you want ( 10<x<14 ) and then we know that if A and A' are complements then P(A) = 1 - P(A')

619snake
08-13-2010, 03:19 PM
thanks a lot for your help, I think I've figured it out!