answer within 3hrs plis
1. a. During a festive season, a logistic company is requested to arrange product delivery from one warehouse to another warehouse 3 times per day which are morning, noon and night. Throughout the year, the shop owner has observed the rate of defective items caused by the delivery time if the product is delivered in the morning, noon, night, at 2%, 1%, and 5% respectively. The shop owner chooses to request the products to be delivered in the morning, noon, night, at 40%, 50% and 10% respectively. Among all products arrived at the warehouse, if a randomly selected product is not defective, propose the best delivery time that he should adopt in order to have a less chance of receiving defective components. The shop owner insists to arrange the delivery in the morning. Obtain a new rate of defective items for him to alert the driver to take extra care in delivery if he wants the probability of delivery in the morning given a randomly selected product is not defective is greater than 0.5. [25 marks) b. A store has selected three top monthly bestselling products, A, B, and C to analyze the monthly income. The monthly income based on the three products is represented by the expression of (RM)27A+125B+512C. Suppose the mean values of each product are 200, 250, and 100 respectively and variance values of each product are 100, 144, and 64 respectively. Discuss the expected value and variance of the total monthly income by providing mathematical values based on dependent and independent properties. Suppose the sale from each product are independent with a normal distribution. The shop owner would like to decide whether or not he should pre- order the three products to stock up beforehand. He will decide to pre-order double if the total sale from these three products is at least RM 100,000.00 per month. Justify on the likelihood that the shop owner would double his order by providing all the probability calculations. Giving the condition that the owner really wants to order more products if the probability is at least 0.3, what is the expected sale per month that the shop owner needs to earn? (30 marks] 2 1. a. During a festive season, a logistic company is requested to arrange product delivery from one warehouse to another warehouse 3 times per day which are morning, noon and night. Throughout the year, the shop owner has observed the rate of defective items caused by the delivery time if the product is delivered in the morning, noon, night, at 2%, 1%, and 5% respectively. The shop owner chooses to request the products to be delivered in the morning, noon, night, at 40%, 50% and 10% respectively. Among all products arrived at the warehouse, if a randomly selected product is not defective, propose the best delivery time that he should adopt in order to have a less chance of receiving defective components. The shop owner insists to arrange the delivery in the morning. Obtain a new rate of defective items for him to alert the driver to take extra care in delivery if he wants the probability of delivery in the morning given a randomly selected product is not defective is greater than 0.5. [25 marks) b. A store has selected three top monthly bestselling products, A, B, and C to analyze the monthly income. The monthly income based on the three products is represented by the expression of (RM)27A+125B+512C. Suppose the mean values of each product are 200, 250, and 100 respectively and variance values of each product are 100, 144, and 64 respectively. Discuss the expected value and variance of the total monthly income by providing mathematical values based on dependent and independent properties. Suppose the sale from each product are independent with a normal distribution. The shop owner would like to decide whether or not he should pre- order the three products to stock up beforehand. He will decide to pre-order double if the total sale from these three products is at least RM 100,000.00 per month. Justify on the likelihood that the shop owner would double his order by providing all the probability calculations. Giving the condition that the owner really wants to order more products if the probability is at least 0.3, what is the expected sale per month that the shop owner needs to earn? (30 marks] 2
