As an engineer working for a water bottling company, you collect the f

Boduszewox6

Boduszewox6

Answered question

2021-11-29

As an engineer working for a water bottling company, you collect the following data in order to test the perfomance of the bottling systems. Plot the data and calculate the mean and standard deviation.
Milliters of Water in the BottleFrequency48513490174952550040505235101851515

Answer & Explanation

Daniel Williams

Daniel Williams

Beginner2021-11-30Added 14 answers

Introduction
To find:
a) To find the mean and standard deviation of the given data.
b) To find the probability of water filled more than 495 ml
Step 2
Given data:
Milliters of Water in the BottleFrequencyfP(X)=XfXP(X)(Xμ)2(Xμ)2P(X)485130.02713.09111,215.583002.82490170.03517.15114,575.484010.14495250.05125.25117,985.496017.26500400.0840121,445.289715.62505230.04623.23124,955.185747.94510180.03517.85128,515.494498.04515150.02914.94132,124.983831.62μ=151.51σ2=36823.44
Mean:
μ=XP(X)
=151.51
Standard deviation:
σ=(Xμ)2P(X)
=36823.44
=191.89
Step 3
b) To find the probability of water filled more than 495 ml
X=495
Z=Xμσ
=495151.51191.89
=1.79
P(Z>1.79)=0.5P(0<Z<1.79)
=0.50.4633
=0.0367
Conclusion
a) Mean =151.51ml and standard deviation =191.89ml
b) The probability of water filled more than 495 ml is 0.0367

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