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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 Scenarios1) Buyers often insist on discounts for large orders. Experience shows that the amountof their required discounts ranges from 0 to 18%, with auniform distribution.a) Write the mathematical expression for the probability density function of thepercent discount.18-0 =18, given that it is uniformly distributed therefore the probability density function is180181)(txfb) What is the probability that a new buyer will expect a discount that is between5% and 12%?Required probability39.0~3889.018718512)125(12abtttP2) A study from Consumer Reports showed that the lifetime of TV sets is normallydistributedwith mean of 8.2 years and standard deviation of 1.3 years. If is desired to offer a replacementguarantee on the 2% of sets with the shortest lifetimes for how longshould TV’s be guaranteed?Givenyearsandyears3.12.8From the normal distribution table the value of z corresponding to probability 0.02is-2.05Finding the corresponding value of x5.5~05.23.12.8xxxzTV’s be guaranteed for 5.5years3) Suppose that weights of bags of potato chips coming from a factory follow a normaldistribution with mean 12.8 ounces and standard deviation .6 ounces. If themanufacturer wants to keep the mean at 12.8 ounces but adjust the standard deviationso that only 1% of the bags weigh less than 12 ounces, how small does he/she need tomake that standard deviation?Givenouncesandounces6.08.12From the normal distribution table the value of z corresponding to probability 0.01is-2.32For x=1234.0~32.28.1212xz

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Statistics

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