Question 3: The number of vehicles that arrives at a toll booth in a certain exit road in t minutes us known to follow a Poisson distribution with man 0.0125t. a. Find the probability that at least 3...

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Extracted text: Question 3: The number of vehicles that arrives at a toll booth in a certain exit road in t minutes us known to follow a Poisson distribution with man 0.0125t. a. Find the probability that at least 3 vehicles arrive in any 20 minutes period. b. The probability that the number of vehicles arrive at the tool booth in q minutes is 0.9. Find the value of q. The time measured in minutes taken by users at in ATM machine is a random variable which is normally distributed with mean u and standard deviation 2.4. If this result from a sample of 90 users is used to construct a 98% interval for u. Find the width of this interval. d. The time taken for customers to decide when using the restaurant menu is normally distributed with mean u minutes and standard deviation 1.9 minutes. It requires having a 95% confidence interval for u with a total width of less than 2.0. Find the least number of observations needed to c. achieve this.