Answer Happy

6. (6 pts) If the production of a specific part for an assembly of components is regarded as a binomial situation where the random variable X represents the number of defective parts in a production run. Suppose the probability of defective in each unit is p. (a) What is the probability of no defectives in a production run of 10 units? (b) Show that the probability of at most one defective in a production run of 20 units is (1−p)19(1+19p). 7. (10 pts) There are 20 students in a lecture group and the probability that an individual student is late is 0.01. (a) Assume that the students arrive individually and the punctuality or otherwise of a student does not affect the probability that another student is late. What is the probability that no students arrive late? (b) Suppose 200 students eventually arrive at the lecture. Use first the binomial and then the Poisson distribution to calculate the probability that none of these students were late. Comment on your results.