Questions on Probability

1. In a pen factory there is a small chance 1/500 for any pen to be defective. The pens are supplied in packs of 10. Use this probability to calculate the approximate number of packets containing no defective, one defective and two defective pens, respectively in a consignment of 20,000 packets [ e^(--0.02) =0.9802 ] Ans. : 19604, 392, 3.92=4 respectively

2. A manufacturer who produces medicine bottles finds that 0.1% of the bottles are defective. The bottles are packed in the boxes of 500 bottles. A drug manufacturer buys 100 boxes from the producer of bottles . Using suitable probability distribution , find how many boxes will contain (i) No defectives, (ii) At least two defectives ? Answer (i) 0.6065 X 100= app 61 bottles, , (ii) 10 bottles app. 3. Mean and standard deviation of chest measurement of 1200 soldiers are 85 and 5 cm respectively. How many of them are expected to have their chest measurement exceeding 95 cm assuming a normal distribution. ( Prob.=0.9772, Answer =1173) 4. In a certain Poisson frequency distribution the frequency corresponding to 2 successes is half the frequency corresponding to 3 successes. Find its mean and standard deviation.( Mean=6, Sd= Sq. root of 6) 5. A soft-drink vending machine is set so that the amount of drink dispensed is a random variable with a mean of 200 ml. And a standard deviation of 15 ml. Find the probability that the average amount dispensed in a random bottle is at least 204 ml.? (