Portfolio 4 Portfolio 4 is due Sunday 11:59am in May 28 and contains 3 exercises. The portfolio should be submitted either as a PDF or as a live script (.mlx file). This portfolio should be formatted so that the start of each question is clearly marked, and the final answer to each question is clearly highlighted. There is no page limit, but you should aim to keep worded responses to questions concise. Solutions to a portfolio from a previous year have been provided to give people an example of portfolio formatting. Q1 - Probability The following probability exercises relate to circuit components that are tested in a production line to check whether they're within tolerence specifications. 50% of componenents produced are resistors which have a 94% chance of being within tolerance specifications, 20% of components are inductors which have a 96% chance of being made to specification and the remaining components are capacitors which have a 98% chance of being made to specification. Please answer the following questions: ⦁ What is the probability that the first three circuit elements on the production line are resistors? ⦁ What is the probabability that the first three circuit elements on the production line are all the same type of element? ⦁ What is the probability that a random circuit elements on the production line is within the tolerance specifications? ⦁ If a circuit element was found to not meet tolerance specifications, what is the probability that the element is a resistor? ⦁ On average, how many circuit elements would go along the production line until 10 elements were found to be outisde of the tolerance specifications? Q2 - Probability Distributions Traffic data was collected from a busy street in New York. It was found that cars pass by at an average rate of 600 cars per hour, with the time between cars being independent. For each question, clearly indicate the probability distrubution being used to solve the problem, solve by hand and then verify your answer using MATLAB. ⦁ What is the probability that there is more than 30 seconds of time between one car and the next? ⦁ What is the probability that 5 or less cars pass by within 1 minute? ⦁ The speed of the cars was found to be normally distributed with the average car speed being , and the variance being . Given a car is speeding if it travelling over , what is the probability that a random car was speeding? ⦁ What is the probability that at least 3 out of 5 random cars are speeding? ⦁ What is the fastest that a car can travel if it is in the lower quartile (slowest 25% of cars)? Q3 - Inference 10 springs have been tested and have had their spring constant recorded. This data has been provided in a .csv file. ⦁ Using MATLAB, import the data using and determine the sample mean and variance (using in-built functions is fine). ⦁ Determine the 95% confidence interval for the spring constant of the springs. ⦁ The spring manufacturer claims that the springs have a spring constant of 10kN/m. Conduct a hypothesis test to see if there is sufficient evidence to suggest that this spring constant is incorrect. Use the comparison between and for your hypothesis test. ⦁ If the sample mean and variance stayed the same, but there were 50 springs, calculate the new 95% confidence intervals and reconduct a hypothesis test. Explain why the confidence interval changes.