The honey farm has installed a filling machine for honey jars that hol

ofodse

ofodse

Answered question

2021-11-27

The honey farm has installed a filling machine for honey jars that hold 500 g of honey. Doris is calibrating the new machine. She sets the machine to a mean of 500 g and performs a test run of 48 jars. The table attached to the quiz post in the Google Classroom shows the results. Assume it is normally distributed.
Determine the mean of the data
Determine the standard deviation of the data.
What is the probability that a jar contains at least 504 g of honey?

Answer & Explanation

Luis Sullivan

Luis Sullivan

Beginner2021-11-28Added 11 answers

Mean of the data
The mean amount of honey in the sample of 48 jars is calculated as
x=499+501+498++502+499+50248
=2399448
=499.875
standard deviation
So the obtained standard deviation is
s2=1n1×[(xix)2]
s2=1481×[(499499.875)2+(501499.875)2++(502499.875)2]
s=2.49468
s=1.579
Probability
Assuming X to be the amount of honey in a jar,
XN(499.875,1.579)
The required probability is given by P(X504).
P(X504)=1P(X504)
=1P(Z504499.8751.579)
=1P(Z2.61)
=10.995473
=0.0045

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