# Probability & Mathematical Statistics : Assignment

Added on - 28 Jan 2020

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ASSESSMENT ITEM 1

TABLE OF CONTENTSQuestion 2........................................................................................................................................3The probability that any person selected at random from the population is a female.................3The probability that any person selected at random from the population is aged between 25and 54...........................................................................................................................................3The joint probability that any person selected at random from the population is a male andaged between 15 and 24...............................................................................................................3The conditional probability that any person selected at random from the population is 25 orover given that the person is a female.........................................................................................3QUESTION 3 Statistical Decision Making and Quality Control....................................................4(A)....................................................................................................................................................41 If management wishes to establish x-bar control limits covering the 95% confidence interval,calculate the appropriate UCL and LCL......................................................................................42 If management wishes to use smaller samples of 16 observations calculate the control limitscovering the 95% confidence interval.........................................................................................43 Management is considering three alternative procedures in order to maintain tighter controlover labor time.............................................................................................................................5(B)....................................................................................................................................................6

Question 2The probability that any person selected at random from the population is a female.Total females= 47Total population= 86Total females/total population= 47/86= 0.54Probability that any female will randomly selected from the population is 0.54. The highest valueof probability is 1and current value is 0.54 which reflect that there is moderate probability thatrandomly women will be selected from the population.The probability that any person selected at random from the population is aged between 25 and54Total population in group of 25 and 54= 16Total population= 86Total population in group/ Total population=16/86=0.18.There is 0.18 probability that there will random selection of any individual that comes in agegroup of 25 to 54.The joint probability that any person selected at random from the population is a male and agedbetween 15 and 24.Total male in age group of 15 to 24= 7Total population= 86Total make in age group/ Total population= 7/86=0.081There is very low probability of 0.081 that any person randomly selected from the age group of15 to 24 will be male.The conditional probability that any person selected at random from the population is 25 or overgiven that the person is a femaleBy applying formula of conditional probability value computed is 0.65. This reflect that there is0.65 probability that person selected at random from the population is 25 or more in age.By applying mentioned formula probability is computed at 0.65.

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