Fall 2017 STATS 230 Applied Statistics Problem 2. (12 points) The Netherlaods is

Question

Fall 2017 STATS 230 Applied Statistics Problem 2. (12 points) The Netherlaods is one of the woeld leaders in the production and sale of Bowers. Suppooe the greenhosse of Rotterdam's Fastastic Flora follow a contisuoas uniform beights of the tulips la the distribution with a lower bound of 6 inches and an upper bound of 16 inches. a. (2 points) Calculate the mean and standard deviation of the distribation of the beights of the tulipe. (Please round your answers to 3 decimal places) b. (2 polnts) What is the probablity that a randoamly selected talip with a beight greater than 10 inches? (16-10) 6 0.6 10 10 e. (2 points) You pick up 3 tulips independently to make a small bouquet. What is the probability that the heights of all 3 tulips are greater than 10 inches? 0.6 3 = 0.aIG d. (2 points) You pick up 49 tulips independently to maker a large bouquet. Let X be the average height of this large bouquet. Is f normally distribated? Please explain. (No credit if no explanation provided) Centrau uruform dustrbhon on h intrval -, and X is tu mean of an idepundervt rondom sample af size n fron ms asHibuhon, then the centra imut thaor em for ne continuuos pproachs standaid

Explanation / Answer

e) from central limit theorum:

E(Xbar) =population mean =11

and s.e(Xbar)= population std deviation/(n)1/2 =2.887/(49)1/2 =0.4124

f) for normal distribution z score =(X-mean)/std deviation

hence P(Xbar>10) =1-P(Xbar<10) =1-P(Z<(10-11)/0.4124)=1-P(Z<-2.4249)=1-0.0077 =0.9923

please revert

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