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Created: Mar 19, 2015
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NASA Atreyu W., Joseph N.
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Result 1: Histogram concen   [Info]
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Result 2: Summary Stats concen   [Info]
Summary statistics:
ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3
CaConc100185.181227306.271785.4767328.5476732171.34131296.0577565.369851361.4276100.31806258.21045

1. The distribution for the Calcium concentration has a bimodial shape, though it seems to be slightly skewed right. The shape of the graph is bimodal with a space between 200 and 225. The center of the graph is 171.34 with a mean of 185.181. The IQR is 258.21-100.32 = 157.9. The upper bound is 258.21+1.5 (157.9)= 495.06 and the lower bound is 258.21-1.5 (157.9)= 21.36. Looking at the summary statistics, since the min and max do not sit outside the bounds, there are no outliers. Since we dont know the cause for the bimodal gap, it is possible that the two peaks of the graph distribution could be differences in gender.

3:The characteristic that might have caused the data shown is the age of the astronuats. Younger astronauts could have less calcium built up, while older ones have more calcium build up due to age.

4: It is important to randomize in order to create a more accurate representation of what the possible calcium concentration for the 3 astronauts might be.

5: I believe we should not use replacement in this population since the same astronaut group cannot go to the ISS twice at the same time.

6: We also have to assume that the astronauts were selected at random and that their calcium levels are independent of each other.

Result 3: Histogram mean concen   [Info]
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Result 4: Summary Stats mean concen   [Info]
Summary statistics:
ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3
mean(Sample(CaConc))1000183.300352397.213748.9613491.5482938182.75167236.8466474.762556311.6092149.19277218.31251

8: The distribution for the sample distribution of the Calcium Concentration has an unimodal shape and looks approximately normal and symmetrical, with no outliers and a center of about 182.751. The IQR is 218.31-149.192= 69.118. The upper bound is 218.31+1.5 (69.118)=321.987 and the lower bound is 149.192-1.5 (69.118)=45.515. Looking at the summary statistics, since the min and max don't sit oustide of the IQR, we do not have any outliers. 

9: CLT tells us that the sum of the means of a large sample size will be approximately normal. Looking at our ressults, our sample distribution looks approximately normal. However it may not be true since our sample size was only 3, reiterated 1000 times. Compared to the original distribution, the original data graph is bimodal.

10: Based on the results, the standard deviation of our original mean 185.18122 over the square root of 100 is 18.518 and our sample mean is 183.300 over the square root of 1000 is 5.7964. The standard deviation of the original mean is larger than the sample mean because  the n value, or sample size, for each distribution is different. The original distribution has a sample size of 3 while the sample distribution has a sample size of 1000.

11-12: a) 85%: 140: 806/1000= 80.6%

b) 80%: 190: 445/1000= 44.5%

c) 75%: 240: 138/1000= 13.8%

d) 70%: 290: 10/1000= 10%

e) 65%:330: 0/1000= 0%

13: Probability of not having an ARFTA failure over a 6-month mission if the recovery rate is 70% is (1-0.010)^12= 0.88638. 

14: It seems surprising, because the probability of ISS of not experiencing a failure is (1-.806)^12= 2.8419783x10^-9.

15: Based on our probabilities of failure for each recovery % and assuming six months between restocking missions from Earth, we decide that a recovery of 70% and threshold concentration of 290, there is less likely of a chance to experience a probability of failure.

Data set 1. NASAUrine Final   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=48702">NASA Atreyu W., Joseph N.</A>

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