3. [Normal approximation). People use the normal distribution to approximate a binomial distribution, known as normal ap

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3 Normal Approximation People Use The Normal Distribution To Approximate A Binomial Distribution Known As Normal Ap 1 (102.71 KiB) Viewed 21 times

3. [Normal approximation). People use the normal distribution to approximate a binomial distribution, known as normal approximation. Recall that a binomial distribution has two parameters, n and p, and a normal distribution has two parameters as well, u and 62. The normal approximation is to connect the u and o? with n and p, such as и u = np and o2 = np(1 – p) Then the probability of a binomial variable x can be computed as b+0.5 - u a -0.5 - u Pr(a < x <b)0 = ") o 0 where the 0.5 is added to make the boundary points a and b to be included in the probability calculation. This addition/subtraction of 0.5 is called continuity correction. Consider the following problem. A textbook has 800 pages, and on each page, one typographical error could occur. Suppose that there are exactly 10 errors randomly located on those pages. (a) Find the probability that 50 randomly selected pages will contain at least two errors. Hyper- geometric distribution is the theoretically accurate distribution to use. (b) Use a binomial distribution to compute the probability in (a). Make necessary assumptions or approximation. (c) Use the normal approximation to calculate the probability in (b).