Statistics Probability

See attached file

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 Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	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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99 273

100

Age	Maori	Non-Maori
0			10	100
	9	92	4	6		99	5	14
9	91	7	3	99	47
99	11	99	45
9	90	73	9	94	34
99034	99	41	8
99002	99	40
9	89	77	99	39
	98	57	99	38
98941	99	37
989	27	99	36
989	13	99	35
12	9	88	96	9	93	42
98	87		993	26
98	84	99	30
15	98	79	99	273
16	98734	99	23
17	98	64	991	76
18	9	85	28	99109
19	9	83	86	99030
20	98	22	98942
21	9	80	61	988	49
9	78	987	54
	97	24	986	60
97	56	985	69
25	9	74	98	48
9	72	52	98399
9	71	98	32
96	95	9	82	43
29	9	67	9	81
96	63	98090
31	96	46	98013
9	62	97934
33	96088	978	53
9	58	97769
95649	97	68
95404	9	75
9	51	97493
948	65	97393
945	70	97288
94257	97176
93925	97057
93573	96931
93200	96796
44	92802	9	66
92377	96494
91922	96325
91433	96142
90906	9	59
90337	95728
50	89719	95493
89047	95237
88315	94957
87516	94650
86642	94314
55	85686	93945
84642	93541
83504	93099
82267	92615
80928	92085
79483	91504
77930	90867
76269	90167
74499	89398
72622	88553
70640	87624
68555	86604
66370	85485
64089	84259
61716	82917
59256	81448
56716	79840
54104	78082
51427	76162
48691	74069
45898	71793
43049	69327
40145	66666
37190	63810
34191	60761
31161	57525
28117	54113
25087	50539
22122	46816
19287	42956
16618	38975
14122	34904
11816	30802
9720	26749
7854	22835
6229	19149
4847	15773
3701	12761
2765	10112
2017	7836
1435	5930
4374
667	3137
434	2183
1471
165	958

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