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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.