After receiving a large shipment of computer chips, 800 chips are randomly selected. If 3 or fewer defective chips are found, the entire lot is accepted without inspecting the remaining chips in the lot. If 4 or more chips are defective, every chip in the entire lot is carefully inspected at the supplier's expense. Assume that the true proportion of nonconforming computer chips being supplied is 0.001. Use the Poisson distribution to approximate the probability the lot will be accepted.

QUESTION 1 a) In the inspection of a fabric produced in continuous rolls, the number of imperfections is a random variable having the Poisson distribution with an average of 0.25 per meter. i) Find the probability that a four-meter long fabric will have no less than five imperfections. (2 marks) ii) Find the probability that there will be at most one imperfection in a 0.5-meter of the fabric. (4 marks) iii) If 10 rolls of 2 meters of fabric are checked, find the probability that exactly nine rolls will have less than three imperfections. (5 marks) b) The actual amount of instant coffee that a filling machine puts into a 150-ml jar is a random variable having a normal distribution with = 1.5 ml. i) If only 7.49% of the jar is to contain less than 150 ml of coffee, what is the percentage of jar that contains between 147 ml and 149 ml? (6 marks) ii) Using the value obtained in (i), what is the probability that the mean of a random selection of 10 jars will be more than 151 ml? Feb 22 (3 marks) QUESTION 1 a) A computer manufacturing company conducts the acceptance sampling for incoming computer chips. The probability of conforming chips is 80%. If three or fewer non- conforming chips are found, the entire lot is accepted without inspecting the remaining chips in the lot. However, if four or more chips are nonconforming, every chip in the entire lot is carefully inspected at the supplier's expense. i) Find the probability of more than 12 chips in the sample of 20 are the conforming chips. (4 marks) ii) Find the mean and standard deviation of the random variable X, as described in (i). (2 marks)