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Effectus [21]
3 years ago
10

Show that the following data are inconsistent: ‘Of a group of 50 students, 23 take mathematics, 14 take chemistry and 17 take ph

ysics. 5 take mathematics and physics, 3 take mathematics and chemistry and 7 take chemistry and physics. Twelve students take none of mathematics, chemistry and physics’. [Hint: see the last example of the section.]

Mathematics
1 answer:
kirill115 [55]3 years ago
5 0

Answer:The following data are inconsistent because the number of students that offer the three subject gives us a negative value. X= -4. Which shouldn't be. Therefore the data are inconsistent.

Step-by-step explanation:

See attached picture for explanations.

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The standard normal table starts at .5 for z=0, meaning its giving us the integral of the standard gaussian from negative infinity to some positive z.  We look for a table entry of 1-.08=.92 and find that at z=1.41.

We knew it was between one and two because the 68-95-99.7 rule tells us one sigma gives a probability of (100-68)/2=16% and two sigma 2.5%, and 8% is in between those.

So our lengths at the ends of the range are 

5.13 - 1.41(0.04) = 5.0736

5.13  + 1.41(0.04) = 5.1864

Rounding, 5.07 to 5.19




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