Type the correct answer in each box. Round the vector's magnitude to the nearest tenth.
1 answer:
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Answer:
(a) The distribution of (Y - X) is <em>N</em> (0.001, 0.0005).
(b) The probability that the pin will not fit inside the collar is 0.023.
Step-by-step explanation:
The random variable <em>X</em> is defined as the diameter of the pin and the random variable <em>Y</em> is defined as the diameter of the collar.
The distribution of <em>X</em> and <em>Y</em> is:
The random variables <em>X</em> and <em>Y</em> are independent of each other.
(a)
Compute the expected value of (Y - X) as follows:
The mean of (Y - X) is 0.001.
Compute the variance of (Y - X) as follows:
The standard deviation of (Y - X) is 0.0005.
Thus, the distribution of (Y - X) is <em>N</em> (0.001, 0.0005).
(b)
Compute the probability of [(Y - X) ≤ 0] as follows:
*Use a <em>z</em>-table for the probability value.
Thus, the probability that the pin will not fit inside the collar is 0.023.
Answer:
a) There are 10 different samples of size 2.
b) See the explanation section
c) See the explanation section
Step-by-step explanation:
a) We need to select a sample of size 2 from the given population of size 5. We use combination to get the number of difference sample.
b) Possible sample of size 2:
Peter Hankish 8 Connie Stallter 6 Juan Lopez 4 Ted Barnes 10 Peggy Chu 6
- Peter Hankish and Connie Stallter ( Mean = (8 + 6)/2 = 14/2 = 7)
- Peter Hankish and Juan Lopez (Mean = (8 + 4)/2 = 12/2 = 6)
- Peter Hankish and Ted Barnes (Mean = (8 + 10)/2 = 18/2 = 9)
- Peter Hankish and Peggy Chu (Mean = (8 + 6)/2 = 14/2 = 7)
- Connie Stallter and Juan Lopez (Mean = (6 + 4)/2 = 10/2 = 5)
- Connie Stallter and Ted Barnes (Mean = (6 + 10)/2 = 16/2 = 8)
- Connie Stallter and PeggyChu (Mean = (6 + 6)/2 = 12/2 = 6)
- Juan Lopez and Ted Barnes (Mean = (4 + 10)/2 = 14/2 = 7)
- Juan Lopez and Peggy Chu (Mean = (4 + 6)/2 = 10/2 = 5)
- Ted Barnes and Peggy Chu (Mean = (10 + 6)/2 = 16/2 = 8)
c) The mean of the population is:
Comparing the mean of the population and the sample; we can say that most of the 2-size sample have their mean higher than that of the population sample. And the variation with the mean is not much. Some sample have their mean greater than population mean, while some sample have their mean greater than the population mean.