quiz 1 equations

Question 1

population mean

Answer 1

μ

Question 2

median

Answer 2

.5(n+1)
= position

Question 3

when distribution is symmetric, then mean and median are

Answer 3

equal

• skewed right: mean greater than median
• skewed left: median greater than mean

Question 4

variance

Answer 4

POPULATION:
std^2=(summation(xi-μ)^2)/N

SAMPLE:
std^2=(summation(xi-μ)^2)/(n-1)

• or just take sqrt of std

Question 5

variance in population vs sample

Answer 5

POPULATION: σ^2

SAMPLE: s^2

Question 6

tcheybysheffs theorem

Answer 6

1-(1/k)^2 of the measurements lie within k standard deviations of mean

μ-ks and μ+ks

i.e. if k=2, then 1-1/4=3/4
if k=3, then 8/9

Question 7

empirical rule

Answer 7

μ+σ= approx 68% of the measurements

μ+2σ= approx 95% of the measurements

μ+3σ=99.7% of the measurements

Question 8

mean symbol if its population or sample

Answer 8

population: µ

sample: x bar (bar on top)

Question 9

R is approximately

Answer 9

4s

s is approx R/4 or R/6 (if data set is large)

Question 10

z-score

Answer 10

SAMPLE:x-xbar/s
POP: x-µ/fancy s

-2 to 2 are not unusual,
shouldn’t be more than 3 in absolute value
- larger than 3 are outliers

Question 11

Position of Q1
Position of Q3

Answer 11

.25(n+1)
.75(n+1)

IF YOU GET TWO NUMBERS FOR THE POSITION:
Interpolatedvalue=lowervalue+d×(uppervalue−lowervalue)

Question 12

sample variance eqn

Answer 12

s^2=(sumxi^2)-(sumofxi/n)^2/(n-1)

Question 13

at LEAST (new)

Answer 13

P(X>n)=1-P(X>n-1)

Question 14

at MOST (new)

Answer 14

P(X</=n)
- take it from the table directly or sum up until you reach the number

Question 15

When to use cumulative or individual probabilities

Answer 15

“less than”, “greater than” w/ range= cumulative probabilities
[SUBTRACT FROM BIGGER]

• “explicit values listed, just giving numbers” : use individual probabilities
  [SUBTRACT FROM SMALLER]

Question 16

REVENUE AND COST EQUATIONS

Answer 16

Revenue: np(R)

Costs: n(C)

another way:
1) find profit using R-C
2) multiply profit by: x(p(x))

Question 17

fewer than

Answer 17

P(X>n)=sum leading until n-1

for example

P(X>2)=P(X=1)+P(X=0)

Question 18

determining if values line up with tcyshebeff or empirical

Answer 18

1) make intervals
2) round them down
3) solve with table

tceyshbeff: as long as the probabilities are bigger than it works

empirical: should resemble the numbers

Question 19

MORE THAN

Answer 19

P(X>1)=1-[P(X<0)]

• treated like a less than

Question 20

independent events related to Poisson distribution

Answer 20

• do the power rule (make the event to the power of n)

i.e. “none of the next 2 …”

[P(X=0)]^2

(because these are independent events)

Question 21

define the variables for hypergeometric

Answer 21

N: total
M: success
k: failures
n: chosen number

Question 22

when is it not >/= or</=

Answer 22

when its MORE THAN or LESS/FEWER THAN (otherwise its always equal to too)

Question 23

what do you need to write before binomial distribution questions

Answer 23

X~(n,p)

Question 24

more than n

Answer 24

P(X>n)=1-P(X=0)-P(X-n)

take the complement of the summation

Question 25

probability distribution for ch 4 content (when ur given 2 options)

Answer 25

p(0)=3C0(1/2)^n

p(X)=nCx(1/2)^n