Of the 2500 accounts of a particular bank, 125 have been fraudulently altered. The alterations are sufficiently subtle that only a detailed audit can...

1. Of the 2500 accounts of a particular bank, 125 have been fraudulently altered. The alterations are sufficiently subtle that only a detailed audit can uncover them. Fifty business accounts are chosen at random for detailed auditing. Let X be a random variable for the number of fraudulently altered accounts in the sample of fifty.
2. (a) ExplainwhyXfollowsahypergeometricdistribution,andgivetheparametersofthedistribution. (b) Find the probability that the sample will contain at least two accounts that have been altered. (c) Can the distribution for X be approximated by the binomial distribution? Explain.

(d) Regardless of your answer in (c), use the binomial distribution to approximate the probability in (b).