Name ID: AMS Extra credit opportunity
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Infinite Finite C.
Note: 2-1414,312-866 Please give answers in terms of radicals.
The central limit theorem and the standard error of the mean σ(x)- (X) -are based on the premise that the population has infinitely many members. When samples are chosen with replacement the population is effectively infinite.
Consider the population of N- 5 objects (1, 2,3,4, 5)
1. Find the population mean
2. Find the population std. deviation ơ
3. Take (with replacement) samples of size n-2 from the above population.

answer is

c) 4

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}