QUESTION 4 A metal boit has a diameter that has a uniform distribution. The mean

Question

QUESTION 4 A metal boit has a diameter that has a uniform distribution. The mean diameter is 4.18 mm vwi a variance of 0.0003 th e a probability is asked for, do not express this as a percentage. Use fully un-rounded values in all calculat and do not specify units or enter text of any kind: The uniform parameter a is equal to ions, but provide answers to the following questions to 2 decimal places The uniform parameter b is equal to The probability that the bolt will ft into a hole that has a diameter of 4.18 mm is

Explanation / Answer

Uniform Distribution
mean = 4.18
variance = 0.0003

E(X) = (1/2)*(a+b)
4.18 = (1/2)*(a+b)
a + b = 8.36
a = 8.36 - b

Var(x) = (1/12)*(b-a)^2
0.0003 = (1/12)*(b-a)^2
b^2 - 2ab + a^2 = 0.0036
b^2 - 2*(8.36 - b)*b + (8.36 - b)^2 = 0.0036
b^2 - 16.72b - 2b^2 + 69.8896 - 16.72b + b^2 - 0.0036 = 0
-33.44b = -69.886
b = 2.09

a = 8.36 - 2.09 = 6.27

The value of a = 2.09 and b = 6.27

P(X < 4.18) = (x-a)/(b-a) = (4.18-2.09)/(6.27 - 2.09) = 0.5

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