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

Answer: Ans:
1. a. it is a problem of means.
c. x bar N(150, 27/sqrt(16))
e. x bar=2500/16=156.25

P(x bar>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