the following questions: 4. Once a week a merchandiser replenishes the stocks of a particular product brand in six stores for which she is responsible. Experience has shown that there is a one-in- five chance that a given store will run out of stock before the merchandisers weekly visit. (a) Which probability distribution is appropriate in this problem? Why? (b) What is the probability that, on a given weekly round, the merchandiser will find exactly one store out of stock? (c) What is the probability that, at most, two stores will be out of stock? (d) What is the probability that no stores will be out of stock? (e) What is the mean number of stores out of stock each week? 7. A Tata truck dealer has established that 5% of new Tata trucks sold are returned for defective assembly repairs within their 12-month warranty period. Assume that the dealer has recently sold eight new Tata trucks. (a) What is the probability that only one of the eight Tata trucks will be returned for defective assembly repairs within its 12-month warranty period? (b) What is the probability that at most two of the eight Tata trucks will be returned for defective assembly repairs within their 12-month warranty period? (c) What is the probability that all eight Tata trucks sold are fault free and will not need repairs due to defective assembly within their 12-month warranty period? (d) If the Tata truck dealer sells 64 new trucks per year, what is the average number of trucks sold that will need assembly defective repairs under their 12-month warranty agreement? 13. A company that supplies ready-mix concrete receives, on average, six orders per day. (a) What is the probability that, on a given day: (i) only one order will be received? (ii) no more than three orders will be received? (iii) at least three orders will be received? (b) What is the probability that, on a given half-day, only one order will be received? (Hint: Refer to the word of caution in section 5.4.) (c) What is the mean and standard deviation of orders received per day? 14. The number of tubes of toothpaste purchased by a typical family is a random variable having a Poisson distribution with an average of 1.8 tubes per month. (a) What is the probability that a typical family will purchase at least three tubes of toothpaste in any given month? (b) What is the likelihood that a typical family will purchase less than four tubes of toothpaste in any given month? 15. A short-term insurance company receives seven motor vehicle claims, on average, per day. Assume that the daily claims rate follows a Poisson process. (a) What is the probability that on a given day no more than five motor vehicle claims will be received? (b) How likely is it that either six or nine motor vehicle claims will be received on a given day? (c) What is the chance that more than 20 motor vehicle claims will be received by the company over any two-day period? (Hint: Refer to the word of caution in section 5.4. attached)