Final answer:
Normal approximation to the binomial is used for the typo question, while normal approximation to the Poisson distribution is used for the flu question, both involving calculating the mean and standard deviation and applying a continuity correction.
Step-by-step explanation:
The probability that at least 100 out of 1000 theses contain typos, given that on average 1 in 10 people make typos, can be found using the normal approximation to the binomial. We calculate the mean (μ = np) and the standard deviation (σ = √(np(1-p))), where n is the number of trials (1000) and p is the probability of making a typo (0.1). For the normal approximation, we also apply a continuity correction since we are approximating a discrete distribution with a continuous one.
For the Poisson distribution scenario, we are given that the average number of persons getting the flu per year is 144. Assuming a Poisson distribution, we want to find the probability of fewer than 280 persons getting the flu over two years. Since the time period is doubled, the mean (λ) is also doubled (288) for the two-year period. We can use the normal approximation to the Poisson distribution because the mean is large. Again, we calculate the mean and standard deviation (σ = √λ), and apply a continuity correction when using the normal approximation to find the probability.