Question

The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a sample 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.

Answer 1

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