Find the probability that: a) No customer patronises the coffee shop in a time interval of 6 minutes. b) At least one customer patronises the coffee shop in a time interval of 12 minutes. c) Between 2 and 4 customer patronises the coffee shop in a time interval of 12 minutes.
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.
b) At least one customer patronises the coffee shop in a time interval of 12 minutes.
c) Between 2 and 4 customer patronises the coffee shop in a time interval of 12 minutes.
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.
b) The operator will receive a total of 3 calls.
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
b) At most two cars arriving during a particular 10-minute interval
c) More than four cars arriving during a 15-minute interval
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 11.00 am on a certain weekday
b) She will receive exactly 3 calls between 10.30 am and 10.40 am
c) she will receive no calls between 10.30 am and 10.40 am
5. The length of houseflies follows a
a) More than 2.28
b) Less than 1.45
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
b) More than 1.06
7. If ?~?(100,16), find:
a) ?(?>104)
b) ?(?<92)
c) ?(?<115)
8. The score of 6000 candidates in a certain examination are found to be approximately normal distributed with a mean of 55 and a standard deviation of 10.
a) If a score of 75 or more is required for passing with distinction, estimates the number of grades with distinction.
b) If 70% of the candidate pass the examination, calculate the probability that from three candidates selected at random, only two candidates pass the examination
c) Calculate the probability that a candidate selected at random has a score between 45 and 65.
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