BUS309 Statistics for Business and Economics I Spring 2019 Dr. James P. Minas Chapter 4 & 5 – Continuous & Discrete Distributions Assignment #3 This assignment is to be undertaken individually and is...

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BUS309 Statistics for Business and Economics I Spring 2019 Dr. James P. Minas Chapter 4 & 5 – Continuous & Discrete Distributions Assignment #3 This assignment is to be undertaken individually and is due at the start of class on Monday April 1st 2019. Any late submissions will only be accepted up until Monday April 8th with a 50% grade reduction, no assignments will be accepted after this date. Your submission should be a hardcopy report containing the answers to all questions presented in the same order they appear in the assignment description. Your answers must be clear, concise and supported by attached output from R (include both code and outputs). 1. A local fast food chain measures the amount of time that it takes to place and prepare an order for a customer. After analyzing the data it has been determined that the place/prepare times follow a Uniform distribution with a minimum place/prepare time of 2 minutes and a maximum place/prepare time of 8 minutes. a) Sketch the distribution (by hand), calculate the mean and include this on your sketch. b) What is the probability that it takes less than 3 minutes to place and prepare an order? c) What is the probability that it takes more than 5 minutes to place and prepare an order? d) What is the probability that it takes between 2.5 and 7 minutes to place and prepare an order? e) The fast food chain wants to publish a service standard on their website i.e. “90% of orders will be placed and prepared within ……. minutes.” Calculate what the service standard should be. f) Simulate the place/prepare time of 100 customers by generating random values from your Uniform distribution. How many of the 100 customers orders took longer than the service standard computed in part e? 2. The housing prices in Brooklyn, New York follow a Normal distribution with a mean of $788,000 and a standard deviation of $39,400. a) Sketch the distribution (by hand), include the mean on your sketch. b) What is the probability that a house in Brooklyn costs less than $720,000? c) What is the probability that a house in Brooklyn costs more than $800,000? d) What is the probability that a house in Brooklyn costs between $750,000 and $850,000? e) The city wants to apply an additional property tax to the most expensive 10% of houses in Brooklyn. Calculate what the cutoff-price is for homes that will be required to pay this new tax. f) Simulate the prices of 50 houses by generating random values from your Normal distribution. How many of the 50 houses are priced above the tax program cut-off computed in part e? 3. Suppose the number of patients visiting a local doctor between 10 am and 1 pm can be modelled with a Poisson distribution with a mean of 22. a) Calculate the standard deviation of the distribution. b) What is the probability that exactly 22 patients visit the doctor between 10am and 1 pm? c) What is the probability that 15 or less patients visit the doctor between 10am and 1 pm (i.e. X=<15)? d)="" what="" is="" the="" probability="" that="" more="" than="" 18="" patients="" visit="" the="" doctor="" between="" 10am="" and="" 1="" pm="" (i.e.="" x="">5)? e) Simulate 100 doctor visit periods by generating random values from your Poisson distribution. In how many of these periods were there more than 18 patients?