The average weight of a bag of potato chips produced by A Ltd is 150g, with a st
ID: 3153859 • Letter: T
Question
The average weight of a bag of potato chips produced by A Ltd is 150g, with a standard deviation of 12g. A random sample of 50 bags was chosen from the production line.
a Which probability distribution do you believe the sample mean will follow (explain briefly to support your argument) and what are the mean and standard deviation of this distribution?
b What is the probability that the sample mean weight will be between 152g and 154g?
c Given that 90% of all the sample mean weights are heavier than K, find the value of K. Keep your final answers to two decimal places.
Explanation / Answer
a.using central limit theorem the sampling distribution of sample mean is approximately normla with mean mu=150 and standard deviation=sigma/root over n
=12/root over 50
=1.69
b.For X=152, z=(152-150)/1.69
=1.18
For X=154, z=(154-150)/1.69
=2.36
Thus P(152<X<154)
=P(X<154)-P(X<152)
=P(z<2.36)-P(z<1.18)
=0.9909-0.8810
=0.1099
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.