A (destructive) tensile test is the standard procedure for testing a cross-wire
ID: 3042700 • Letter: A
Question
A (destructive) tensile test is the standard procedure for testing a cross-wire weld. Suppose a certain weld is designed to withstand a force with mean 0.8 kilonewtons (kN). To check the quality of welds, a manufacturer randomly selects 25 welds (every hour) and performs a tensile test on each weld. Suppose the force distribution is normal with standard deviation 0.15 kN. (1 pt.) a) What is the probability that the sample mean force in the test is more than 0.79 kN? (1 pt.) b) If the mean force required (for the 25 welds) is between 0.75 and 0.9 kN, the process is allowed to continue. Otherwise, it is shut down. What is the probability that process is allowed to continue. (1 pt.) c) Assuming that the sample mean force is more than 0.79 kN, what is the probability that it is also more than 0.84 KN?Explanation / Answer
a)
b)
c)
hence probability that sample mean force is more than 0.84 given it is greater than 0.79
=P(X>0.84|X>0.79)=0.0912/0.6306 =0.1446
for normal distribution z score =(X-)/ here mean= = 0.800 std deviation == 0.150 sample size =n= 25 std error=x=/n= 0.0300 probability = P(X>0.79) = P(Z>-0.33)= 1-P(Z<-0.33)= 1-0.3694= 0.6306Related Questions
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