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Probability : Maximium Likelihood Estimator and p-Values

A GMAT test center reports that out of 200 students who took a GMAT test at the test center 60 scored above 600.

a) Derive the maximum likelihood estimator (MLE) of p, the proportion of students scoring above 600. What is the ML estimate of n*p(1-p)

b) What is the MLE of P(X<50)?

c) Test if the proportion of students scoring abve 600 is lower than 0.4 at the center at alpha = 0.01 using p-value.

Please see the attached file for the fully formatted problems.

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Maximium Likelihood Estimator and p-Values are investigated. The solution is detailed and well presented.

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