Please help with the second and third part A detector located underground in a s
ID: 3203884 • Letter: P
Question
Please help with the second and third part
A detector located underground in a salt mine near Cleveland detected a burst of 8 neutrinos within a particular 10-minute interval. Most interestingly, this was at the same time as the optical observation of Supernova 1987A. Find the probability of observing 8 or more neutrinos in one day. if. on average, the detector would normally find 2 neutrino interactions per day. Find the probability of observing 8 or more neutrino interactions in a ten-minute time interval. Again, assume that the experimenters expected, on average. 2 neutrino interactions per 24 hours. Discuss the statistical significance of this observation of 8 neutrinos within 10 minutes. State clearly what is significant (or insignificant) about it. Advice: If the probability of observing 9 or more events is significantly less than that for exactly 8 events, then, to a very good approximation, the probability of 8 or more is simply that for 8. Check this as an approximation by calculating the probability of 9 events (and then 10) and compare. If the approximation seems good, then use it. You will save a lot of work and gain some insight as well.Explanation / Answer
2)
Overall there are 1440 minutes in 24 hours. If within 1440 minutes, there are 2 neutrino interactions, then there would be 0.013888889 during 10 minute interval. Hence, =0.013888889 and we would have to calculate for x=1, 2, 3, 4, 5, 6 and 7 and then subtract it from 1 and so we would get 8 or more. Calculating that, we get the probability to be 0.000000000004257039.
3)
The probability of it is close to 0 and this proves that it was statistically significant.