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Statistics question, Basic Statistics

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1. A sample from 16 different farms across Quebec shows that the hay production in bales per acre is normally distributed N(100,50).
a. (2p )What is the probability that a random farm from this sample produces less than 80 bales/acre?



b. (2p) What is the probability that another random sample of nine farms has an average of less than 80 bales/acre?



c. (1p) Is the population mean known?



d. (2p) What can we learn from the central limit theorem in this case?



e. (3p) Calculate a 90 % confidence interval around the population mean.




f. (2p) Interpret: what does your answer in e) mean?


g. (2p) These nine farms were actually a pilot study. What is the minimal sample size needed to compute a 95 % confidence interval around the population mean?

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