Probability Distributions, Normal Distribution, Sampling Distribution

Question 1

Discrete Probability Distribution?

Answer 1

table, graph data set that specifies all possible values of a discrete random variable along with their corresponding probabilities
-frequency of something occurring over the total number of data pieces

Question 2

what to do when finding probabilities of greater than or less than questions?

Answer 2

-add probabilities bellow or above the given value/ variable

Question 3

Normal Distribution?

Answer 3

• most important distribution

- determined by the parameters of the variance and mean

Question 4

Is normal distribution continues or discrete?

Answer 4

• continuous

- calculate probabilities that fall within a range of values

Question 5

What is the reason the probability of X being equal to a specific value is 0 in a continuous distribution?

Answer 5

-a continuous random variable can take on an infinite number of values, therefore the probability of the variable taking a specific value is 0

Question 6

Characteristics of a normal distribution?

Answer 6

-symmetrical around the mean
-mean median and mode are all equal
-percentage of values falling within 1,2 and 3 standard deviations of the mean is
1 std= 68.3%
2 std= 95.4%
3 std= 99.7%

Question 7

Variance and spread?

Answer 7

low variance= low spread

high variance= high spread

Question 8

Graph of 2 normal distributions with different means and the same variances/ std?

Answer 8

-look the exact same due to variance but placed on the graph in different spots due to the different mean values

Question 9

Graph of 2 normal distributions with the same means and different variances/ std?

Answer 9

-graphs look different, but are surrounded in the same area on the graph due to having the same mean value

Question 10

Standard Normal Distribution?

z = x-u/σ

Answer 10

• standardize every normal distribution so each has a mean of 0 and a standard deviation of 1 by computing the z score
• from this we can determine probabilities of values from a table created for the standard normal distribtuion

Question 11

Standard normal distribution mean value and standard deviation value?

Answer 11

mean= 0

standard deviation= 1

Question 12

-1 to 0 (0-1) is how much of a normal distribution?

Answer 12

50%

Question 13

Value of the probability of everything under a normal distribution curve?

Answer 13

Equal to 1

Question 14

Sampling Distribution?

Answer 14

distribution of all possible values of a statistic that can be computed from all samples of the same size randomly drawn from the same population

Question 15

What 3 things do we want to know about a given sampling distribution?

Answer 15

1. mean
2. variance
3. functional form of the distribution (how its shape looks like)

Question 16

Sampling Distribution mean of population and the mean of the
“means”? variance?

Answer 16

-always the same

variance is population is larger than the variance of the sample population

Question 17

Standard deviation vs standard deviation of the mean?

Answer 17

-distribution of the sample means is tighter than the distribution of the entire original data set (b/c original data contains small and large data values

Question 18

Another term for standard deviation of the mean?

Answer 18

Standard error of the mean

Question 19

Central Limit Theorem?

Answer 19

• Given a population of any non-normal distribution with a mean of u and variance of o2, the sampling distribution of the mean, computed from samples of size n from this population will be approximately normally distributed when the sample size is large
• rule of thumb is greater than 30
• increase the sample size, you become more normally distributed