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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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- A mining company finds that daily lost-work injuries average 1.2. If the local union contract has a clause requiring that the mine be shut down as soon as three workers incur lost-work injuries, on what percentage of the days will the mine be operational throughout the day?Can you provide any explanation for these results? For THE 3 TABS BELOW: Tab 1, Tab 2 & Tab 3 TAB 1. Year Age of Miss America Murder by steam, hot vapors and hot objects Dev(x) Dev(y) CP 1999 24 7 1.9 2.5 4.69 2000 24 7 1.9 2.5 4.69 2001 24 7 1.9 2.5 4.69 2002 21 3 -1.1 -1.5 1.69 2003 22 4 -0.1 -0.5 0.05 2004 21 3 -1.1 -1.5 1.69 2005 24 8 1.9 3.5 6.60 2006 22 4 -0.1 -0.5 0.05 2007 20 2 -2.1 -2.5 5.32 2008 19 3 -3.1 -1.5 4.78 2009 22 2 -0.1 -2.5 0.23 Mean 22.1 5 Sum 34.45 Standard Deviation 1.75810 2.25227 Covariance 3.45 Correlation Coefficient 0.87013 0.87013 TAB 2 Year Letter in Winning World of Scripps National Spelling Bee Number of people Killed by venomous spider Dev(x) Dev(y) CP 1999 9 6 -1.0 -1.4 1.36 2000 8 5…Suppose that, as Human Resources Manager of a firm with more than 10,000 employees, you are interested in understanding: (i) what fraction of those employees are satisfied with their working conditions and (ii) how many hours your employees spend each evening reading and writing work-related emails. You do not have the budget to survey all employees, so you a sample of 200 employees. The results reveal that: (i) 125 of the sample employees are satisfied with their working conditions and (ii) sample employees spend, on average, 2.2 hours each evening reading and writing work-related emails, with a sample standard deviation of 0.4 hours. 1. Construct and interpret a 95% confidence interval for the proportion (p) of employees who are satisfied with their working conditions. 2. Construct and interpret a 95% confidence interval for the mean number of hours employees spend reading and writing work-related emails each evening.
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