Im stuck in this statistics problem

In summary, the weight of items produced by a production line follows a normal distribution with a mean of 12 ounces and a standard deviation of 2 ounces. Quality control requires the weight to be within 8 and 16 ounces. The probability of 3 out of 7 items fulfilling the requirements is 0.9544. It is unclear if the requirement is for exactly 3 out of 7 items.
  • #1
619snake
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0

Homework Statement



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.
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 items will fulfill quality control requirements.

What I have to the moment is:
X~n(12,2)
P(x<16) - P(x<8)
z=(16-12)/2
z=2

z= (8-12)/2
z=-2

p(z<2)-P(z<-2)
=.9772-.0228
=.9544

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

Those where other requirements of the problem. I'm stuck at the supposing, can't decide if it is binomial or not, and how to start the procedure
 
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  • #2
So you calculated the probability of success for each trial to be 0.9544? That takes care of the supposing part. Now figure out what the 3 out of 7 means.

.. personally I can't tell. Is it asking for _exactly_ 3 out of 7?
 

Related to Im stuck in this statistics problem

What is statistics?

Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, and presenting numerical data. It is used to make informed decisions and draw conclusions about a population based on a sample.

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