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Gnom [1K]
3 years ago
13

Find Y. Round to the nearest tenth.

Mathematics
1 answer:
Andreas93 [3]3 years ago
6 0

Answer:

y=27.8

Step-by-step explanation:

  • 8^2=17^2+16^2-2(16)(17)cosY
  • 8^2-17^2-16^2/-2(17)(16)=cosY
  • -481/-544=cosY
  • 0.8842=cosY
  • Y is about 27.8
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The probability that the assembly line will be shut down is 0.00617.

Step-by-step explanation:

We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.

Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.

Let X = <u><em>Number of bottles in the sample that are not within specification</em></u>.

The above situation can be represented through binomial distribution;

P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....

where, n = number of trials (samples) taken = 12 bottles

             x = number of success  = 2 or more bottles

            p = probabilitiy of success which in our question is probability that  

                 bottles are not within specification, i.e. p = 0.01

So, X ~ Binom (n = 12, p = 0.01)

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                 = 1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})

                 = <u>0.00617</u>

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