Plan to spend about 1 hour on application of Normal

1. Coin is tossed 200 times. Estimate probability that number of heads is between 95 and 105, included – that is to say that it deviates from 100 by 5 at most. Use Binomial distribution. Compare resultrd to Normal approximation. What is error, compared to Binomial?
2. 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? Use Binomial distribution. Compare resultrd to Normal approximation. What is error, compared to Binomial?
3. Someone tells you that he repeated Mende's experiment with green/yellow peas and in 987 peas counted 738 were yellow and 249 were green.
   1. Do these results agree with Mendel?
   2. What is probability of such-good-or-better match to Mendel?
   3. What would you think (about this person)?
4. Repeat the exercise assuming that on total, 100 peas were evaluated and the distribution was 77:23
5. 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%
6. (Extension of Problem 3 from Drift section) A genetically isolated populations was founded seven generations ago by 250 people. Number of people in subsequent generations were 400, 700, 1400, 2800, 6000, 12000 and currently population comprises 20000 people. What are the chances that an allele with initial frequency of 0.02 will increase its frequency at least twice? Compare results with Pardo et al. (2005).