Normal Distribution, Sampling Distribution, Central Limit Theorem

Question 1

Often called the “bell curve” and Gaussian Distribution and is determined by the mean and standard deviation.

Answer 1

Normal Distribution

Question 2

Who created the bell curve?

Answer 2

Carl Friediech Gauss (A German Mathematician)

Question 3

Properties of Bell-Shaped

Answer 3

• Bell-Shaped
• Symmetrical
• Mean, Median, and Mode coincide in the center
• Standard Deviation determines the width
• Tails of curve flatten out indefinitely
• Curve is asymptotic
• Area of curve is ONE

Question 4

A normal distributioj whose mean is 0 and standard deviation is 1.

Answer 4

Standard Normal Distribution

Question 5

What do you call thre middle of a bell-curve?

Answer 5

unimodal

Question 6

The conversion of any x-value of a normal distributiij to its standard normal variable

Answer 6

Standardization

Question 7

Determines the proposition of values that fall within certain distances of the mean

Answer 7

Empirical Rule

Question 8

68% equals to

Answer 8

mean + standard deviation

Question 9

mean + 2 (standard deviation)

Answer 9

95%

Question 10

99.7% equals to

Answer 10

mean + 3 (standard deviation)

Question 11

Has a long-tail to the right and median plus mode is to the left of the mean

Answer 11

Positively Skewed

Question 12

Has a long tail to the left and meadian plus mode is to the left of the mean.

Answer 12

Negatively Skewed

Question 13

Percentage of 0 to 1

Answer 13

34%

Question 14

Percentage of 1 to 2

Answer 14

13.5%

Question 15

Percentage of 2 to 3

Answer 15

2.35%

Question 16

Percentage of the ends

Answer 16

0.15%

Question 17

Standardization Formula

Answer 17

z = (x - mean) / standard deviation

Question 18

A measure of relative standing with respect to random variable

Answer 18

z-value or z-score

Question 19

Formula in converting z-score to x-value

Answer 19

x = z (standard deviation) + mean

Question 20

Formula of finding percentile with two similar z-scores

Answer 20

= (z1 + z2) / 2

Question 21

What side do you shade at Case 1?

Answer 21

Left

Question 22

What side do you shade at Case 2?

Answer 22

Right

Question 23

What part to you shade in case 3?

Answer 23

Inside

Question 24

What part do you shade in Case 4?

Answer 24

outside

Question 25

Totality of items under consideration

Answer 25

Population

Question 26

Subset of population

Answer 26

Sample

Question 27

Any characteristic of a population

Answer 27

Parameter

Question 28

Any characteristic of a sample

Answer 28

Statistic

Question 29

Difference between the sample statistic and the population parameter

Answer 29

Sampling Error

Question 30

The probability distributioj if a statistic

Answer 30

Sampling Distribution

Question 31

The standard deviatioj of the samplinh distribution

Answer 31

Standard Error

Question 32

Formula of Variance for Sampling Distribution

Answer 32

= variance / n (if n is infinite)

= variance / n (N - n/n -1) (if n is finite)

Question 33

Random sample of size n are drawn from any population with a finite mean and a standard deviation, n is latge, and sample mean is approximately distributiin with mean and standard deviation

Answer 33

Centeal Limit Theorem

Question 34

When is Central Limit Theorem applied?

Answer 34

1.) If sample population is normal
2.) “ “ “ is almost symmetric
3.) “ “ “ is skewed, when n >30 or n = 30

Question 35

CLT Formula

Answer 35

= standard deviation / squareroot of n

Question 36

Formula if only sample standard deviation s is known

Answer 36

= s / squareroot of n