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The mean yield of a chemical process is being research by an engineer. From
previous experience with this process the standard deviation of yield is known
to be 3. He would like to be 99% confident that the estimate point should be
accurate within yield point with the value of one.
(i) Examine the error and then analyze how large a sample is necessary for
this research?
(ii) Suppose that an engineer reduced the sample size to 20. If it was found
that the sample mean is 10 and a standard deviation of 1.6, find a 99%
confidence interval for the mean yeild.
a. What is the probability that exactly 20 seeds germinate.
b. What is the probability that 20 or more seeds germinate
c. What is the mean number of seeds that germinate
d. Determine the variance and standard deviation in the number of seeds that germinate.
A class contains 10 men 20 women of which half of men and half of the women have brown eyes a person is selected one by one find the probability that
1. First one has brown eye and second and third are not brown eyes
2. First two are women and third and forth are men
A class contains 10 men 20 women of which half of men and half of the women have brown eyes a person is selected one by one find the probability that
1. First one has brown eye and second and third are not brown eyes
2. First two are women and third and forth are men
Two dice were rolled, find the probability that: -
1. Sum is 7 given that product is 10
2. Sum is less than 4 given that product is 4
3. Product is 12 given that sum is 8
4. Sum is divisible by 2
Suppose that a factory has two machines, Machine A and Machine B, both producing iPhone touch screens. Forty percent of their touch screens come from Machine A and 60% of their touch screens come from Machine B. Ten percent of the touch screens produced by Machine A are defective and five percent of the touch screens from Machine B are defective. If I randomly choose a touch screen from those produced by both machines and find that it is defective, what is the probability that it came from machine A and also find the probability that it came from machine B ?
1. First one has brown eye and second and third are not
brown eyes
2. First two are women and third and forth are men
17.2 22.1 18.5 17.2 18.6 14.8 21.7 15.8 16.3 22.8
24.1 13.3 16.2 17.5 19.0 23.9 14.8 22.2 21.7 20.7
13.5 15.8 13.1 16.1 21.9 23.9 19.3 12.0 19.9 19.4
15.4 16.7 19.5 16.2 16.9 17.1 20.2 13.4 19.8 17.7
19.7 18.7 17.6 15.9 15.2 17.1 15.0 18.8 21.6 11.9
and the values are
A 66 67 75 76 82 84 88 90 92
B 64 66 74 78 82 85 87 92 93 95 97
Test whether the two populations have the same variance at the 5%
level of significance (F=3.36) at 5% level for v1=10 and v2 = 8.
Calculate the Skewness by using the Karl-Pearson method for the following frequency distribution and interpret the result.
Ages(Years)
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
No.of Men
29
176
208
173
82
40
15
3
