1. The numbers of customers who patronise a coffee shop follow Poisson distribution with mean of 20 per hour. Find the probability that: a) No customer patronises the coffee shop in a time interval of 6 minutes. (0. 13 53) b) At least one customer patronises the coffee shop in a time interval of 12 minutes. (0.9817) c) Between 2 and 4 customer patronises the coffee shop in a time interval of 12 minutes. (0.5373) 2. The number of telephone calls received by an operator follows a Poisson distribution with mean 4. Find the probability that: a) The operator will not receive any call. (0.0183) b) The operator will receive a total of 3 calls. (0.1954) 3. Cars arriving at a toll at an average rate of 30 per hour. Assuming the number of cars arriving at the toll follows a Poisson distribution, find the probability that a) No car arrives during a particular 5-minute interval (0.0821) b) At most two cars arriving during a particular 10minute interval (0.125) c) More than four cars arriving during a 15-minute interval (0.868) 4. A receptionist in a trading company receives 6 telephone calls on average between 10.30 am and 11.00 am on a weekday. Find the probability that a) She will receive 2 or more between 10.30 am and 1 1.00 am on a certain weekday (0.983) b) She will receive exactly 3 calls between 10.30 am and 10.40 am (0.180) c) she will receive no calls between 10.30 am and 10.40 am (0.135) 5. The length of houseflies follows a normal distribution with mean 2 and variance 0.09. find the probability that the length of a housefly caught at random is: a) More than 2.28 (0.1762) b) Less than 1.45 (0.0336) 6. The thickness of paper produced by a type of machine follows a normal distribution. If the mean thickness of the paper is 1.05 and its standard deviation is 0.02. Determine the probability that the thickness of a sheet of paper taken at random is: a) Between 1.10 and 1.12 (0.006) b) More than 1.06 (0.3085)