The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a s
ample of size 100, resulting in the following frequencies:
Number of particles: 0, 1, 2, 3, 4, , 5, 6, 7
Frequency: 1, 2, 3, 12, 11, 15, 18, 10
Number of particles: 8, 9, 10, 11, 12, 13, 14
Frequency: 12, 4, 5, 3, 1, 2, 1
(a.) What proportion of the sampled wafers had at least one particle? At least five particles?
(b.) What proportion of the sampled wafers had between five and ten particles, inclusive? Strictly between five and ten particles?
(c.) Draw a histogram using relative frequency on the vertical axis. How would you describe the shape of the histogram.
Number of particles: 0, 1, 2, 3, 4, , 5, 6, 7
Frequency: 1, 2, 3, 12, 11, 15, 18, 10
Number of particles: 8, 9, 10, 11, 12, 13, 14
Frequency: 12, 4, 5, 3, 1, 2, 1
(a.) What proportion of the sampled wafers had at least one particle? At least five particles?
(b.) What proportion of the sampled wafers had between five and ten particles, inclusive? Strictly between five and ten particles?
(c.) Draw a histogram using relative frequency on the vertical axis. How would you describe the shape of the histogram.
1 answer:
Answer:
1. a, 99% b71%
2. 64%, 44%
3. Number of particles 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
frequencies: 1, 2, 3, 12, 11, 15, 18, 10, 12, 4, 5, 3, 1, 2, 1
Relative frequencies 0.01, 0.02,0.03,0.12,0.11,0.15, 0.18,0.1, 0.12,0.04, 0.05,0.03,0.01,0.02,0.01
Step-by-step explanation:
Number of particles: 0, 1, 2, 3, 4, , 5, 6, 7
Frequency: 1, 2, 3, 12, 11, 15, 18, 10
Number of particles: 8, 9, 10, 11, 12, 13, 14
Frequency: 12, 4, 5, 3, 1, 2, 1
we solve by saying that . one of th smaples wafer is with any particles. we get the proportion by subtracting 1 from the total divided by 100
100-1/100
.99
at least five particles , then we can subtract the number of those with particles less than five from 100 , divided by 100
100-(11+12+3+2+1)=71/100
0.71 or 71%
b. those particles within 5 and 10 inclusive
15+18+10+12+4+5=64/100
0.64
0r 64%
five and 10 exclusively will be
18+10+12+4=44/100
0.44
44%
c. Draw an histogram. first we have frequency table first
Number of particles 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
frequencies: 1, 2, 3, 12, 11, 15, 18, 10, 12, 4, 5, 3, 1, 2, 1
Relative frequencies 0.01, 0.02,0.03,0.12,0.11,0.15, 0.18,0.1, 0.12,0.04, 0.05,0.03,0.01,0.02,0.01
Relative frequencies is derived by dividing each frequencies over the total frequencies
wecan say that it is unimodal or say that it is slightly positively skewed
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