Plan to spend about 1 hour on application of Normal

1. The frequency of a genetic variant is 0.01 How many people you need to sample to have 95% probability to have at least THREE carriers?
   1. STANDARDUse Binomial distribution to compute exact estimate
   2. STANDARDCompare exact Binomial to Poissin and Normal approximations (lectures). Which one worked better? Why?
2. STANDARD Coin is tossed 100 times. Estimate probability that number of heads is between 45 and 55, included – that is to say that it deviates from 50 by 5 at most. Use Binomial distribution. Compare results to Normal approximation. What is error, compared to Binomial?
3. STANDARD Someone tells you that he repeated Mendel's experiment with green/yellow peas and in 1000 peas counted 710 were yellow and the rest were green. Apparently this is not quite 3:1 (750:250). 40 yellow plants are "missing" (and thus 40 green are "extra"). Assuming that 3:1 holds, what is the probability to observe this or even more extreme deviation from the expected?
4. STANDARD Repeat the exercise assuming that in total, 100 peas were evaluated and the experimental distribution was 71:28.
5. HIGH (Extension of Problem 3 from Drift section) A genetically isolated populations was founded by 230 people. Number of people in subsequent generations were 400, 700, 1500, 3000, 6000, 12000 and currently population comprises 20000 people. What are the chances that an allele with initial frequency of 0.01 (in founder generation) will increase its frequency at least twice?
6. Briefly read the paper of Pardo et al. (2005) and compare your and Pardo's results.
7. Read the paper of Pardo et al. (2005) and compare your and Pardo's results.
8. STANDARD The frequency of a genetic variant is 0.05 How many people you need to sample to have 95% probability to have at least TEN carriers?
   1. STANDARDUse Binomial distribution to compute exact estimate
   2. STANDARDUse Poisson approximations
   3. HIGH or MEDIUM (MEDIUM = when solution was numeric)Use Normal approximations
   4. Compare exact Binomial results to Poisson and Normal approximations (lectiures). Which one worked better? Why?
9. STANDARD Frequency of a mutant allele is 0.01. What should be sample size to have at least 10 carriers with probability
   1. 50%
   2. 95%
   3. 99%