Ucas Exam - Stats And Mechanics

Question 1

Standard deviation (words)

Answer 1

The root of: the mean of the squares minus the square of the means

Question 2

Standard deviation formula

Answer 2

√(Σfx^2/Σf)-(Σfx/Σf)^2

Question 3

Linear interpolation formula

Answer 3

LB+(PL/GF x CW)

Question 4

Coded data

Answer 4

y = (x-a)/b

Question 5

Mean of coded data

Answer 5

ȳ = (x̄-a)/b

Question 6

Standard deviation of coded data

Answer 6

σy = σx/b

Question 7

Where to draw cross on cumulative frequency graph

Answer 7

Upper end point of the class width

Question 8

Where to draw cross for frequency polygon

Answer 8

Midpoint of class width

Question 9

Frequency formula

Answer 9

Frequency = frequency density x class width

Question 10

What formula is for mutually exclusive probability events

Answer 10

P(A U B) = P(A)+P(B)

Question 11

What formula is for statistically independent probability events

Answer 11

P(A n B) = P(A) x P(B)

Question 12

What is the addition formula for P(A U B)

Answer 12

P(A) + P(B) - P(A n B)

Question 13

What is the multiplication formula for P(B|A)

Answer 13

P(B n A)/ P(A)

Question 14

Binomial PD without calc

Answer 14

nCr x P(failure)^no.failures x P(success)^no.success

Question 15

Binomial distribution, what does each letter mean

Answer 15

X ~ B(n,r)

n = number of trials
p = probability of success

Question 16

Binomial PD

Answer 16

P(X=y)

Question 17

Binomial CD

Answer 17

P(X ≤ y)

Question 18

Normal distribution p(1 sd from mean)

Answer 18

68%

Question 19

Normal distribution p(2 sd from mean)

Answer 19

95%

Question 20

Normal distribution p(3 sd from mean)

Answer 20

99.7%

Question 21

Expression for normal distribution and what does each letter mean

Answer 21

X ~ N(μ, σ^2)

Mu = mean
σ = standard deviation

Question 22

What is the probability in Inverse normal

Answer 22

The area to the left

Question 23

What is the standard normal distribution

Answer 23

Z ~ N(0,1^2)

Question 24

What is the formula for z in standard normal

Answer 24

Z = (X - μ)/σ

Question 25

How to find missing mean or sd value normal distribution

Answer 25

Use inverse to find the Z value and sub into the formula

Question 26

What is going from binomial to normal called

Answer 26

Continuity correction

Question 27

Binomial to normal conversions

Answer 27

Mean - np
Variance - np(1-p)

Question 28

when can a binomial distribution be approximated to a normal

Answer 28

p close to 0.5
n is large

Question 29

conditions for binomial distribution

Answer 29

• fixed number of trials
• 2 possible outcomes
• fixed probability of success
• trials are independent

Question 30

what does binomial distribution measure

Answer 30

p(X≤x)

Question 31

p(B|A)

Answer 31

probability of b occurring given that A has already occurred

Question 32

formula for p(B|A)

Answer 32

p(B n A)/p(A)

Question 33

moment

Answer 33

force x distance

Question 34

rigid body in equilibrium

Answer 34

resultant force and resultant moments = 0

Question 35

maximum friction

Answer 35

μR

Question 36

static rigid body

Answer 36

• stationary
• resultant force = 0
• resultant moment = 0

Question 37

further kinematics - displacement (constant velocity)

Answer 37

r = r0 + vt

Question 38

Further kinematic - constant acceleration

Answer 38

r = r0 + (ut + 0.5at^2)

Question 39

Sample mean normal distribution

Answer 39

x̄ ~ N(μ, σ^2/n)