5. Airport authority of MADRAS claims that the average time taken by their passengers to complete the boarding process is less than the average of all other Airports in the country 60 mins. A random sample passengers, who used the Madras Airport in a particular day, gave the following boarding time distribution. (' Time taken to complete No of persons the boarding process(mins) 8. 16 0-20 20-40 40-60 39 60-80 38 80-100 15 Calculate the arithmetic mean and standard deviation of this distribution and use these values to test their claim at 5% level of significance. Comment their claim based on your investigation.
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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