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Set2_Spring2007_Solutions

Set2_Spring2007_Solutions - Homework Set#2 NAME_Solutions...

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Homework Set #2 NAME:___________ ___ Solutions ____________ CM:__ ____ __________ MA 223, Engineering Statistics Spring 2008; 15 points possible Due date: Tuesday , March 18 at the BEGINNING of class . You may work together on thinking through these problems, but what you turn in must be your own individual write up and work. Please show as much work as possible. When in doubt about what to include, include it! It’s much easier to give partial credit when the work is all available. Please clearly label your graphs including axes … Please attach your Maple work at the end of the homework set . 1. [+3] Timmy Daydream has trouble paying attention in his statistics class. Let denote the number of minutes that Timmy is able to focus on the material during any given 50 minute lecture. The value of varies from lecture to lecture. The density function for the distribution of is given by: , where is some constant. (a) Determine the value of the constant such that ( x ) is a valid density function. Express k correct to at least four decimal places. We want to find such that . In Maple: > solve(int(k*(exp(-x/10)-exp(-x)),x=0..50)=1,k); > evalf(%); So, . (b) Below, sketch the graph of the density function over the support region and shade the region corresponding to the proportion of lectures during which Timmy concentrates on fewer than 10 minutes of the material. Clearly label your axes and points on your graph. (c) What proportion of the lectures sees Timmy able to concentrate for more than 30 minutes? Express your answer correct to at least four decimal places. From Maple: > evalf(int(solve(int(k*(exp(-x/10)-exp(-x)),x=0..50)=1,k)*(exp(-x/10)- exp(-x)),x=30..50)); 1 9 10 e ( ) -5 e ( ) -50 0.1119492311 0.04819316037
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2 2. [+2] The Salty Spud Potato Chip Company uses a machine to fill 8 oz. bags with Super Salty chips.
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