II. A m Porn resched drgn evolution over the last 2000 turn (yenarm). It. ls knc

Question

II. A m Porn resched drgn evolution over the last 2000 turn (yenarm). It. ls knc dragon trainer fro rom data collected from the time dragons were firnt bred that the mean body length IrOm Tern in 30' with standard deviation 3.97 The trainer collecta a random sample of 30urn. Tarthanl, a tirn ih erunl to one Earth yeunr, thus the random sample wan 3o draggons ple of 30 turns. [In (o) Define the Central Limit Theorem (CLT) (b) Consider the random sample of 30 turns. Describe t mean (what should it leal I'l

Explanation / Answer

SolutionA:

CLT:

For n>30 large sample CLT holds good.

as the sample size gets large enough,the sampling distribution becomes almost normal regardless of shape of population.

The mean of the sample means will be the population mean mu.

the standard deviation of the sample means will apprroach sigma/sqrt(n)

Solutionb:

n=30

mean=35

std error=sigma/sqrt(n)

=3.97/sqrt(30)

=0.72482

Solutionc:

P(X<36)

z=x-mean/stderror

=36-35/3.97/sqrt(30)

=1.38

P(Z<1.38)=0.9162

ANSWER :0.9162

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