Heres a list of my answers that i can remember (This is edexcel paper 2, stats and mechanics)
Stats:
1a) (proof)
b) 1.588
c) this would have no effect on the estimation for standard deviation
2a) no correlation
b) There is a negative correlation between these two variables, meaning that the higher the pressure, the lower the rainfall (or whatever variables there were, it might have been some other variables)
c) 1020hPa
d) The beaufort conversion for windspeed is a discrete, categoric variable therefore it would make no sense to find a linear regression for this with another variable.
3a) 12<=x<=32
b) Cannot be independent, as for independence x=21.6, cant have 0.6 students (x must be an integer)
4a) H1: p (not equal to) 0.25
b) O<=X<=6 ( i think, not 100% certain i remember that one correctly) OR 20<=X<=50
c) probability of incorrectly rejecting H0=0.0333
d) falls out of critical region, result is insignificant, failed to reject H0, insufficient evidence to support his belief
5a) P(X=0)=5/14, P(X=1)=15/28, P(X=2)=3/28 (needs to be in the typical probability distributiion format, but these are the numbers i got)
b) 0.0184
Mechanics)
1a) they are both running the same race, so must both cover the same distance overall
b)0.8ms^-2
c)100m
d)3.92=X
2a)h=78.4m
b) Time = 5 seconds
c) force of air resistance against the motion of the particle could be considered
3a) (proof)
b) 8ms^-2
c) (98/3)m
4a) 0.5ms^-2
b) a1 would be less than a
c) the force of air resistance varies with the velocity of the car, hence modelling the resistance against the cars motion to being of a constant magnitude is unrealistic
(PS: these are only my answers if i remember them correctly, i may very well be incorrect so take this with a grain of salt)