. Margarete, an experienced knitter, makes one wrong stitch in every 197 stitches, on average. To judge the quality of her work, suppose we examine a simple random sample of 1000 stitches. Let X be the number of wrong stitches in a sample of size 1000. (a) Explain any additional assumptions needed to justify using a binomial distribution as a probability model for the random variable X. (b) Compute the probability that there will be no more than two wrong stitches in the sample examined. Round your answer to three decimal places. (c) Find the mean and standard deviation for the random variable X.

3. Margarete, an experienced knitter, makes one wrong stitch in every 197 stitches, on average. To judge the quality of her work, suppose we examine a simple random sample of 1000 stitches. Let X be the number of wrong stitches in a sample of size 1000. (a) Explain any additional assumptions needed to justify using a binomial distribution as a probability model for the random variable X. (b) Compute the probability that there will be no more than two wrong stitches in the sample examined. Round your answer to three decimal places. (c) Find the mean and standard deviation for the random variable X. Enter your answer for question 3(c) on the final exam PDF. The parameters for the random variable X are . mean u = ; and . standard deviation o = Type your answer in the form H, O