Statistics Probability

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	16
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]

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]

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