The owner of a car dealership has just employed a new salesman. The dealer believes that...

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The owner of a car dealership has just employed a new salesman. The dealer believes that salesmen can be categorised as either great, good or poor. In the past, 20% of salesmen have been great, 50% good, and 30% poor. It is assumed that the number of cars sold by each category of salesmen follows a Poisson distribution. On average, great salesmen sell 1 car every other day, good salesmen 1 car every 4 days, and poor salesmen 1 car every 8 days. After 24 days on the job, the new salesmen has sold 10 cars. (i) At the time the new salesman was hired, compute: (a) the expected number of cars he will sell in his first 24 days; (b) the probability that he will sell exactly 10 cars in his first 24 days. (ii) After the new salesman's first 24 days, compute: (a) the expected number of cars he will sell in his next 24 days; (b) the probability that he will sell exactly 10 cars in his next 24 days. The owner of a car dealership has just employed a new salesman. The dealer believes that salesmen can be categorised as either great, good or poor. In the past, 20% of salesmen have been great, 50% good, and 30% poor. It is assumed that the number of cars sold by each category of salesmen follows a Poisson distribution. On average, great salesmen sell 1 car every other day, good salesmen 1 car every 4 days, and poor salesmen 1 car every 8 days. After 24 days on the job, the new salesmen has sold 10 cars. (i) At the time the new salesman was hired, compute: (a) the expected number of cars he will sell in his first 24 days; (b) the probability that he will sell exactly 10 cars in his first 24 days. (ii) After the new salesman's first 24 days, compute: (a) the expected number of cars he will sell in his next 24 days; (b) the probability that he will sell exactly 10 cars in his next 24 days.

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