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# ____________________ 115.101 Statistics for Business ID Number: ASSIGNMENT 2 DUE 3 JAN 2013 RD Q1 A study at a semiconductor manufacturing plant...

A small trucking company has determined that on an annual basis the distance travelled per truck is normally distributed with a mean of 100.0 thousand kilometres and a standard deviation of 20.0 thousand kilometres.
(a) What proportion of trucks travel more than 150,000 km in the year?
(b) What distance will be travelled by 99% of trucks in the year?
(c) What is the probability that the average distance travelled in one year by the fleet of 8 trucks does not exceed 120,000 km?
Name: ____________________ 115.101 Statistics for Business ID Number: A SSIGNMENT 2 D UE 3 RD J AN 2013 Q1 A study at a semiconductor manufacturing plant analyzed whether the presece of particles on the die affected the quality of the wafer. The results were: Condition of Die Quality No particles Particles Good 348 14 Bad 92 44 (a)According to the table, what is the probability that a randomly-chosen wafer was produced from a die that had particles? .................................................................................................................................... ............................................................................................................................... [2] (b) If you know that a wafer is bad, what is the probability, according to the table, that it was produced from a die that had particles? .................................................................................................................................... ............................................................................................................................... [2] (c) Explain, with reference to your answers to (a) and (b) above, whether the two events: a bad wafer and a die with particles: are independent. .................................................................................................................................... ............................................................................................................................... [2] Q2 The data file LIFETABLE.xls gives the number out of 100,000 NZ-born males who are still alive at each age between 0 and 100, separately for Māori and non-Māori ( Source: StatisticsNZ ). Use the table to calculate, separately for Māori and non-Māori: (a) the probability that they will reach the age of 50; P(reach50 | Māori) =. ................................................................................................. P(reach 50 | non-Māori) =. .................................................................................... [2] (b)the probability that they will reach the age of 60; P(reach 60 | Māori) =. ................................................................................................ P(reach 60 | non-Māori) =. .................................................................................... [2] (c)the probability that they will reach the age of 60 given that they have reached 50. P(reach 60 | reach50 and Māori) =. ............................................................................ P(reach 60 | reach50 and non-Māori) =. ................................................................ [2] 115.101/Ass2/1203 1
Name: ____________________ 115.101 Statistics for Business ID Number: Q3 Check\$mart’s records show that 58% of their customers pay only the minimum amount on their credit card each month. (a) What is the probability that, from a random sample of 6 Check\$mart credit-card holders, all will pay only the minimum amount? .................................................................................................................................... .................................................................................................................................... ............................................................................................................................... [2] (b) What is the probability that, from a random sample of 6 Check\$mart credit-card holders, at least two will pay only the minimum amount? .................................................................................................................................... .................................................................................................................................... ............................................................................................................................... [2] (c) Why can we not work out, from the information given, the probability that a customer pays more than the minimum amount? .................................................................................................................................... ............................................................................................................................... [2] Q4 A small trucking company has determined that on an annual basis the distance travelled per truck is normally distributed with a mean of 100.0 thousand kilometres and a standard deviation of 20.0 thousand kilometres. (a) What proportion of trucks travel more than 150,000 km in the year? .................................................................................................................................................. .................................................................................................................................................. .................................................................................................................................... ............................................................................................................................... [3] (b) What distance will be travelled by 99% of trucks in the year? .................................................................................................................................................. .................................................................................................................................... ............................................................................................................................... [3] (c) What is the probability that the average distance travelled in one year by the fleet of 8 trucks does not exceed 120,000 km? [ Note: part (c) needs material from CAST 6.1.6 ] .................................................................................................................................................. .................................................................................................................................................. ............................................................................................................................... [4] + + + + + + 115.101/Ass2/1203 2

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