An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2...

PLEASE ANSWER PARTS D AND E ONLY.

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Extracted text: An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1).="" c.="" what="" sample="" size,="" n,="" is="" required="" for="" the="" estimator="" to="" be="" within="" one="" foot="" of="" the="" true="" mean="" with="" 95%="" probability?="" (i.e.="" find="" the="" value="" of="" n="" that="" satisfies="" p(|x="" –="" µ|="">< 1)="0.95.)" d.="" suppose="" the="" ecologist="" ends="" up="" sampling="" n="9" alligators="" and="" calculates="" a="" sample="" mean="" of="" ī="10.4" feet.="" construct="" a="" 95%="" confidence="" interval="" for="" the="" population="" mean.="" e.="" give="" an="" interpretation="" for="" the="" interval="" obtained="" in="">