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Furkat [3]
3 years ago
15

Carlo puts tins into small boxes and into large boxes. He puts 6 tins into each small box. He puts 20 tins into each large box.

Carlo puts a total of 3000 tins into the boxes so that number of tins in small boxes : number of tins in large boxes = 2:3 Carlo says that less than 30% of the boxes filled with tins are large boxes. Is Carlo correct? You must show all your working.
Mathematics
1 answer:
meriva3 years ago
8 0

Answer: Carlo is incorrect

Step-by-step explanation:

3000/(2+3) = 600 (each ratio)

2:3 = 2(600):3(600) = 1200:1800

1200/6 = 200 small boxes

1800/20 = 90 large boxes

290 boxes altogether (large and small)

(large boxes/boxes altogether)x100

(90/290)x100 = 31%

31%>30%

Therefore Carlo is incorrect

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Suppose a large shipment of laser printers contained 18% defectives. If a sample of size 340 is selected, what is the probabilit
Anestetic [448]

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The probability that the sample proportion will be greater than 13% is 0.99693.

Step-by-step explanation:

We are given that a large shipment of laser printers contained 18% defectives. A sample of size 340 is selected.

Let \hat p = <u><em>the sample proportion of defectives</em></u>.

The z-score probability distribution for the sample proportion is given by;

                         Z  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}}  }  ~ N(0,1)

where, p = population proportion of defective laser printers = 18%

            n = sample size = 340

Now, the probability that the sample proportion will be greater than 13% is given by = P(\hat p > 0.13)

         P(\hat p > 0.13) = P( \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}}  } > \frac{0.13-0.18}{\sqrt{\frac{0.13(1-0.13)}{340}}  } ) = P(Z > -2.74) = P(Z < 2.74)

                                                                      = <u>0.99693</u>

The above probability is calculated by looking at the value of x = 2.74 in the  table which has an area of 0.99693.

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