An article in the Los Angeles Times (Dec. 3, 1993) reports that 1 in 200 people carry the defective gene that causes inherited colon cancer. In a sample of 1000 individuals, what is the approximate distribution of the number who carry this gene? Use this distribution to calculate the approximate probability that a.? ?Between 5 and 8 (inclusive) carry the gene. b.?? t least 8 carry the gene.

Problem 83E Answer: Step1: We have An article in the Los Angeles Times (Dec. 3, 1993) reports that 1 in 200 people carry the defective gene that causes inherited colon cancer. In a sample of 1000 individuals, 1 That is n = 1000, p = 200 = 0.005 And q = 1 - p = 1 - 0.005 = 0.995 We need to find, what is the approximate distribution of the number who carry this gene Use this distribution to calculate the approximate probability that a. Between 5 and 8 (inclusive) carry the gene. b. At least 8 carry the gene. Step2: Consider a random variable “X” it follows normal distribution with mean “np” and variance “npq”. A probability density function of 2ormal distribution is given by 1 2(npq)) f(x/np,npq) = 2(npq)e , Where, np = mean of the normal distribution npq = variance of the normal distribution npq = standard deviation of the normal distribution. a). Consider, Mean = np = 1000×0.005 = 5 Variance = npq = 1000×0.005×0.995 = 4.975 Standard deviation = npq = 1000 × 0.005 × 0.995 = 2.2305 Now, P(Between...