NOTE: Answers using z-scores rounded to 3 (or more)
decimal places will work for this problem.
The population of weights for men attending a local health club is
normally distributed with a mean of 167-lbs and a standard
deviation of 27-lbs. An elevator in the health club is limited to
32 occupants, but it will be overloaded if the total weight is in
excess of 5824-lbs.
Assume that there are 32 men in the elevator. What is the average
weight beyond which the elevator would be considered
overloaded?
average weight =
What is the probability that one randomly selected male health club
member will exceed this weight?
P(one man exceeds) =
(Report answer accurate to 4 decimal places.)
If we assume that 32 male occupants in the elevator are the result
of a random selection, find the probability that the elevator will
be overloaded?
P(elevator overloaded) =
(Report answer accurate to 4 decimal places.)
If the elevator is full (on average) 6 times a day, how many times
will the elevator be overloaded in one (non-leap) year?
number of times overloaded =
(Report answer rounded to the nearest whole number.)
Let X represent the full height of a certain species of tree.
Assume that X has a normal probability distribution with a mean of
105.2 ft and a standard deviation of 4.5 ft.
A tree of this type grows in my backyard, and it stands 94 feet
tall. Find the probability that the height of a randomly selected
tree is as tall as mine or shorter.
P(X<94) =
My neighbor also has a tree of this type growing in her backyard,
but hers stands 104.3 feet tall. Find the probability that the full
height of a randomly selected tree is at least as tall as
hers.
P(X>104.3) =
1)a ) average weight = 5824/32=182
b) P(one man exceeds) =P(X> 182)=P(Z>0.556)=0.2893
c) P(elevator overloaded) = P(Xbar>182)=P(Z>(182-167)*sqrt(32)/32)=P(Z>3.143)=0.0008
d) number of times overloaded = 6*365*0.0008=1.752~2
2)
a)probability that the height of a randomly selected tree is as
tall as mine or shorter.
P(X<94) = P(Z<-2.49)=0.0064
b)
probability that the full height of a randomly selected tree is at least as tall as hers.
P(X>104.3) = 0.5793
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