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# Bumper Installation

The time taken to install bumpers on cars passing through a particular assembly line is normally distributed with mean time u=2.00 minutes and standard deviation =36 minutes. A sample on n=100 is obtained and a mean bumper installation time X-bar will be calculated.
1. Find the value of standard deviation X bar.
Determine the probability that Xbar will
2. Lie between 2.07 and 1.93
3. Exceed 1.98 minutes
4. Fall below 1.94
5. Lie between 2.02 and 2.08
6. Fall above 2.05

#### Solution Preview

I doubt the standard deviation of 36 minutes, which is even far higher than the mean value. Because the Sm of sample is Sd/SQRT(N)=36/SQRT(100)=3.6 minutes, then the answer to 1~6 will all be 100%.
<br>Therefore, I think it might be 0.36 minute or 36 seconds, but it can't be decided from your working (it's not clear how you reach 0.27)
<br>However, I'll take 0.36 minute as the standard deviation. If the true value is 36 seconds=36/60=0.6 minute, you only need to replace standard deviation with 0.6 minute and finish the calculation as follows:
<br>
<br>M=2.00, N=100 ...

#### Solution Summary

The solution discusses the time taken to install bumpers on cars passing through a particular assembly line is normally distributed with mean time u=2.00 minutes and standard deviation =36 minutes. A sample on n=100 is obtained and a mean bumper installation time X-bar will be calculated.
1. Find the value of standard deviation X bar.
Determine the probability that Xbar will
2. Lie between 2.07 and 1.93
3. Exceed 1.98 minutes
4. Fall below 1.94
5. Lie between 2.02 and 2.08
6. Fall above 2.05

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