State the empirical rule as specialized to variables.
for any variable whose distribution the following properties hold. answer options: is triangular, is uniform, is bell shaped
property 1: approximately all possible observations lie within one standard deviation to either side of the mean.
property 2: approximately of all possible observations lie with in two standard deviations to either side of the mean.
property 3: approximately of all possible observations lie within three standard deviations to either side of the mean.
a. 89%, 99.7%, 100%, 75%, 95%, 68%
b. 99.7%, 68%, 95%, 100%, 75%
c. 95%, 99.7%, 100%, 68%, 89%

bellshaped

a) 68

b) 95

c) 99.7

Step-by-step explanation:

A bell shaped distribution is a normal distribution.

Those percentages: 68, 95 and 99.7 correspond to the values that lies around the mean within one, two and three standard deviations.

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}