Question: An elevator has a maximum occupancy of 16 people and a weight limit of
2500 lbs. The average weight of the population is 150 lbs, with a standard deviation of 27
lbs, and the distribution of weight in the population is approximately normal. Suppose
that a random sample of size 16 people is chosen.
a) Is this a problem about means or proportions? If proportions, do we meet the
criteria for the Binomial situation?
b) What is the population distribution?
c) What symbol do we use to represent the sample statistic?
d) What is the sampling distribution of the sample statistic?
e) What is the probability that a random sample of 16 people will have an average
weight in excess of 2500 lbs (the elevator’s weight limit).
f) What is the probability that any individual weighs more than 156.25 lbs
Statistics homework help Edit
1. a. it is a problem of means.
c. x bar N(150, 27/sqrt(16))
e. x bar=2500/16=156.25
z=(x bar - 150)/(27/sqrt(16))=(156.25 - 150)/(27/sqrt(16))=0.93
P(x bar>156.25)=P(z>0.93)=0.5-0.3238=0.1762(Ans.) Edit
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