1.Three bolts are randomly chosen from a box containing 7 bolts, two of which ha

Question

1.Three bolts are randomly chosen from a box containing 7 bolts, two of which have stripped threads. (a) What is the exact probability that only one of the bolts selected has stripped threads. (b) What type of distribution does the number of bolts in a sample of size 3 having strupped threads actually have?

2.The fill volume of cans filled by a certain machine is normally distributed with mean 12.05 oz. and standard deviation 0.03 oz. (a) What proportion of cans contain less than 12 oz (b) The process can be adjusted through calibration. To what value should the mean be set so that 99% of the cans will contain 12 oz or more? (c) If the process mean remains at 12.05 oz what must the standard deviation be so that 99% of the cans will contain 12 oz or more?

Explanation / Answer

2.
Mean ( u ) =12.05
Standard Deviation ( sd )=0.03
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 12) = (12-12.05)/0.03
= -0.05/0.03= -1.6667
= P ( Z <-1.6667) From Standard Normal Table
= 0.0478                  
proportion of cans contain less than 12 oz is 4.78%
b.
P( X >= 12 ) = P ( Z < X ) = 0.01
Value of z to the cumulative probability of 0.01 from normal table is -2.326
P( X-u/s.d < X - U /0.03 ) = 0.01
That is, ( 12 - U /0.03 ) = -2.3263
--> ( 12 - U ) = -2.3263*0.03
--> ( 12 - U /0.03 ) = -3.4316
--> U = 0.0698 + 12 = 12.06984                  

c.
P ( Z < X ) = 0.01
Value of z to the cumulative probability of 0.01 from normal table is -2.326
P( X-u/s.d < X - 12.05/ s.d ) = 0.01
That is, ( 12 - 12.05/ s.d ) = -2.3263
--> s.d = ( 12 - 12.05 ) / -2.3263
--> s.d = ( -0.0500000000000007 ) / -2.3263
--> s.d = 0.0215                  

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