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Probability and Statistical Analysis of Real-World Scenarios

An assignment applying probability and statistics to real-world cases.

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    Probability and Statistical Analysis of Real - World Scenarios 1) Buyers often insist on discounts for large orders. Experience shows that the amount of their required discounts ranges from 0 to 18%, with a uniform distribution . a) Write the mathematical expression for the probability density function of the percent discount. 18 - 0 =18 , given that it is uniformly distributed therefore the probability density function is         18 0 18 1 ) ( t x f b) What is the probability that a new buyer will expect a discount that is between 5% and 12%? Required probability 39 . 0 ~ 3889 . 0 18 7 18 5 12 ) 12 5 ( 1 2          a b t t t P 2) A study from Consumer Reports showed that the lifetime of TV sets is normallydistributed with mean of 8.2 years and standard deviation of 1.3 years. If is desired to offer a replacement guarantee on the 2% of sets with the shortest lifetimes for how longshould TV’s be guaranteed? Given years and years 3 . 1 2 . 8     From the normal distribution table the value of z corresponding to probability 0.02 is - 2.05 Finding the corresponding value of x 5 . 5 ~ 05 . 2 3 . 1 2 . 8 x x x z          TV’s be guaranteed for 5.5years 3) Suppose that weights of bags of potato chips coming from a factory follow a normal distribution with mean 12.8 ounces and standard deviation .6 ounces. If the manufacturer wants to keep the mean at 12.8 ounces but adjust the standard deviation so that only 1% of the bags weigh less than 12 ounces, how small does he/she need to make that standard deviation? Given ounces and ounces 6 . 0 8 . 12     From the normal distribution table the value of z corresponding to probability 0.01 is - 2.32 For x=12 34 . 0 ~ 32 . 2 8 . 12 12            x z

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