Unit 4

Question 1

density curves

Answer 1

mathematical models representing the distribution of our variables values

Question 2

what can a smooth curve tell us?

Answer 2

the proportion of observations that fall below a certain value

Question 3

what are the two important properties of density curves?

Answer 3

a density curve is always positive
(never falls below the x- axis, can have (-) y values)
has an area of 1 underneath it
(represents 100% of the data)

Question 4

what is a uniform distribution between 0 and 1?

Answer 4

a density curve for which each number between 0 and 1 is equally likely

Question 5

what is proportion?

Answer 5

area of a rectangle (normally in %)

Question 6

how do you calculate the area of a triangle?

Answer 6

area = 0.5bh

Question 7

what are 5 characteristics of a normal distribution?

Answer 7

bell shaped
symmetric
heavy in the middle and light on the ends
density curves, therefore never falls below the x-axis
has an area underneath equal to 1

Question 8

how do you calculate the area of a triangle?

Answer 8

area = 0.5bh

Question 9

what is a parameter?

Answer 9

any mathematical calculation performed on a population

Question 10

what are the two parameters?

Answer 10

mean and standard deviation

Question 11

what is μ?

Answer 11

mean (the center)

Question 12

what is σ?

Answer 12

population standard deviation (how concentrated the distribution is about the mean

Question 13

what are the two parameters?

Answer 13

mean and standard deviation

Question 14

what is a statistic?

Answer 14

a mathematical calculation performed on a sample

Question 15

the two parameters correspond to two statistics, what are they?

Answer 15

X̄ and s

Question 16

what is X̄?

Answer 16

the sample mean that corresponds to μ

Question 17

what is s?

Answer 17

the sample standard deviation that corresponds to σ

Question 18

what is a big difference between μ and σ?

Answer 18

μ value can take any positive or negative value
σ value cannot be negative

Question 19

how is this read?
X ~ N(μ, σ)

Answer 19

X is normally distributed with a mean of μ and a standard deviation of σ

Question 20

what is the 68%, 95% and 99.7% rule?

Answer 20

a normal density curve will have approximately
68% of its data falling within 1 standard deviation from the mean
95% of its data falling within 2 standard deviations from the mean
99.7% of its data falling within 3 standard deviations from the mean

Question 21

what does the standard normal table do?

Answer 21

gives us the area or proportion of observations from negative infinity to some value z, which is called a z-score

Question 22

when an area is to the right, how do we write that proportion?

Answer 22

P(Z > z)

Question 23

what will the proportion of observations at a certain point be?

Answer 23

ALWAYS ZERO
(lines don’t have any area)