The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.46. Part a) What is the probability that the time between consecutive customers is less than 15 seconds? Part b) Find the probability that the time between consecutive customers is between ten and fifteen seconds. Part c) Given that the time between consecutive customers arriving is greater than ten seconds, what is the chance that it is greater than fifteen seconds?
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- The number of cars arriving at a given intersection follows a Poisson distribution with a mean rate of 4 per second. What: is the probability that 3 cars arrive in a given second? is the probability that 8 cars arrive in three seconds? is the probability that more than 3 cars arrive in a period of two seconds?An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean = 117 cm and standard deviation = 5.2 cm. Find the probability that one selected subcomponent is longer than 120 cm. Find the probability that, if four subcomponents are randomly selected, their mean length exceeds 120 cm. Find the probability that if four subcomponents are randomly selected, all four have lengths that exceed 120 cm.An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean = 117 cm and standard deviation = 5.2 cm. Find the probability that, if four subcomponents are randomly selected, their mean length exceeds 120 cm. Find the probability that if four subcomponents are randomly selected, all four have lengths that exceed 120 cm.
- Suppose that an airline quotes a flight time of 2 hours 10 minutes between two cities. Furthermore, suppose that historically flight records indicate that the actual flight time between the two cities, X, is uniformly distributed between 2 hours and 2 hours 20 minutes. Expressing time in minutes: a) Discuss the probability curve of X. b) Find the probability that a randomly selected flight between the two cities will be at least five minutes late. c) Calculate the mean flight time and the standard deviation of the flight time.The number of supermarkets in the City of East Tampa follows a Poisson process with the mean number of supermarkets equal to 0.12 supermarkets per square mile. Assuming that the population is evenly spread across the city, does it meet the food desert criterion that at least 33 percent of the population lives more than 1 mile from a supermarket? Hint: Think about the connection between the percent of the population that lives more than 1 mile from a supermarket and the probability that there are no supermarkets within 1 mile of a particular resident of East Tampa. 4.The average monthly income of the employees of ABC, Inc. is Php.20,000.00 with a standard deviation of Php.550. Assume that the monthly income of the employees of the company is monthly distributed. If an employee of the company is randomly selected, what is the probability that its monthly income is greater than Php.21,000.00? and what if it is less then Php. 21,500.00
- Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Furthermore, suppose that historical flight records indicate that the actual flight time between the two cities, x, is uniformly distributed between 2 hours and 2 hours, 20 minutes (uniform distribution). Letting the time unit be one minute, Find the probability that a randomly selected flight between the two cities will be at least five minutes late (greater than 2 hours 15 minutes). What is the probability the plane will arrive plus or minus 1 standard deviation away from the mean? (Hint: Calculate the mean and standard deviation. Add the standard deviation to the mean to get plus 1 standard deviation away from the mean and subtract the standard deviation from the mean to get minus 1 standard deviation from the mean. Then use these two numbers as your a and b),The number of traffic accidents at a certain intersection is thought to be well modelled by a Poisson process with a mean of 3.5 accidents per year. (a) Find the mean waiting time between accidents. (b) Find the probability that less than one month elapses between accidents. (c) If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean 117 cm and standard deviation 5.2 cm. a) Find the probability that one selected subcomponent is longer than 120 cm. b) Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120 cm. c) Find the probability that if four subcomponents are randomly selected, all four have lengths that exceed 120 cm.
- Assume that the amount of time, in hours, that college students spend per week on homework is normally distributed with a mean of 15 hours and a standard deviation of 3 hours. If 75 students are selected at random, what is the probability that they average: more than 14 hours per week on homeworkbetween 14 and 16 hours per week on homeworkless than 15.5 hours of homework per weekAnswer in complete sentences. Be sure to include all relevant calculations.The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5-minute period, Find the expected value and standard deviation. What is the probability that 2 customers will arrive in a 5-minute period? What is the probability that no more than 2 customers will arrive in a 5-minute period? What are the underlying assumptions that allow us to consider this phenomenon as a Poisson distribution?The number of accidents that occur at an express way is Poisson distributed with a mean of 4 per week.Find the probability of no accidents in one week.