Suppose you are an employee with the Ministry of Transport. The Ministry is interested in determining...

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Suppose you are an employee with the Ministry of Transport. The Ministry is interested in determining whether significant road maintenance is necessary on a particular stretch of road. In addition to assessing current damage to the road, the ministry would like an accurate understanding of the frequency with which the road is used, and they give you the task of figuring this out. You set up a camera to record passing vehicles for an entire year, and find that on average, 90 vehicles pass the camera per day, with a standard deviation of 3 vehicles. Let X = the number of vehicles that pass the intersection per day. a) [1 mark] In one sentence, explain why X is not normally distributed. b) [1 mark] What is the probability that in a random sample of 40 days, 85 cars pass the intersection on average? Please provide only a single number. Do not show any work. Hint: This is something you can figure out without using any formulae. All you need are some definitions and some logic. The words "on average" are key here. c) [4 marks] What is the probability that in a random sample of 40 days, fewer than 91 cars pass the intersection on average? Hint: start by declaring an appropriate random variable. That random variable will have two parameters; do not round either of them. [1 mark] Declare the random variable of interest: [1 mark] Show the probability you are asked to calculate: [1 mark] Calculate that probability (show at least one step): [1 mark] Final answer (rounded to 4 decimal places): d) [1 mark] What is the probability that in a random sample of 40 days, 90 or fewer cars pass the intersection on average? Please provide only a single number. Do not show any work. Hint: This is something you can figure out without using any formulae. All you need are some definitions and some logic. The words "on average" are key here. Suppose you are an employee with the Ministry of Transport. The Ministry is interested in determining whether significant road maintenance is necessary on a particular stretch of road. In addition to assessing current damage to the road, the ministry would like an accurate understanding of the frequency with which the road is used, and they give you the task of figuring this out. You set up a camera to record passing vehicles for an entire year, and find that on average, 90 vehicles pass the camera per day, with a standard deviation of 3 vehicles. Let X = the number of vehicles that pass the intersection per day. a) [1 mark] In one sentence, explain why X is not normally distributed. b) [1 mark] What is the probability that in a random sample of 40 days, 85 cars pass the intersection on average? Please provide only a single number. Do not show any work. Hint: This is something you can figure out without using any formulae. All you need are some definitions and some logic. The words "on average" are key here. c) [4 marks] What is the probability that in a random sample of 40 days, fewer than 91 cars pass the intersection on average? Hint: start by declaring an appropriate random variable. That random variable will have two parameters; do not round either of them. [1 mark] Declare the random variable of interest: [1 mark] Show the probability you are asked to calculate: [1 mark] Calculate that probability (show at least one step): [1 mark] Final answer (rounded to 4 decimal places): d) [1 mark] What is the probability that in a random sample of 40 days, 90 or fewer cars pass the intersection on average? Please provide only a single number. Do not show any work. Hint: This is something you can figure out without using any formulae. All you need are some definitions and some logic. The words "on average" are key here.

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a X is not normally distributed because the number of vehicles passing the intersection per day is a ... View the full answer