[20 points] Suppose that the weights of people who work in an office building ar

Question

[20 points] Suppose that the weights of people who work in an office building are normally distributed with a mean of = 165 lb and a standard deviation of -25 lb. [4 points each] 3. (a) What is the probability that one person, selected at random from the building, weighs (b) Suppose that three people are selected independently of each other. Find the probability (c) Find the probability that a sample of three people will have a mean weight greater than (d) What is the conceptual difference between parts (b) and (c), i.e. how are the events (e) Have you ever ridden in an elevator and read a sign stating its maximum load and more than 200 lb? that all three weigh more than 200 lb, i.e. find P(Xi > 2000 X2 > 200 r 200 lb. different? x, > 200). wondered about the chances the elevator would be overloaded? What is the chance that the total weight of five people is more than 1000 lb, i.e. what is P(X, +...+ X, > 1000)? Hint- try to re-express this as an X-style problem.

Explanation / Answer

from central limit theorum:

for n=5 people

mean =165

and std error of mean =std deviation/(n)1/2 =25/(5)1/2 =11.1803

here for weight of 5 people to be greater then 1000

mean weight of 5 people should be greater then 1000/5 =200

hence required probability =P(Xbar>200) =1-P(Xbar<200) =1-P(Z<(200-165)/11.1803) =1-P(Z<3.1305)

=1-0.9991 =0.0009

therefore chance that weight of 5 people is more then 1000 lb is =0.0009

please revert for any explanation required.

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