chem125ps2[1] - Solutions to PS #2 5.20) Our data has a...

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Solutions to PS #2 5.20) Our data has a Gaussian distribution, with a mean of 69” and a standard deviation of 2”. Given a random sample of 1000 people, how many are a) 67-71”, b) > 71”, c) > 75”, d) 65-67”? a) This is just the integral covering one standard deviation on both sides. From Appendix A, we get that this corresponds to 68.27%, which is about 683 people. b) First we figure out how many people aren’t within one standard deviation, which is equal to (1 – 68.27%), or 31.73%. Half of these are above 71”, and half are below 67”. So percentage above is 0.5*31.73%, which corresponds to 15.865%, or about 159 people. c) Like b, except now it’s three standard deviations. Percentage > 75” or < 63” is equal to (1 – 99.73%), or 0.27%. Half this is 0.135%, which is about 1 person in our sample of 1000. d) Now we want to know how many people are between one and two standard deviations short. Break this up into pieces: 95.45% are within 2 standard deviations on either side, half of this is people between 65” and 69” (47.725%).
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chem125ps2[1] - Solutions to PS #2 5.20) Our data has a...

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