Acceleration is simplified by assuming it is the constant -g
a=-g we integrate this with respect to time to get v...
v=-gt+C where C is the initial velocity in this case 14ft/s so
v=-gt+14 integrate again to get the height function
h=(-gt^2)/2 +14t +C we are not given an initial height so C is 0
h(t)=14t-gt^2/2 letting g=32 and neatening up a bit...
h(t)=14t-16t^2
X=17
Angle E= 155°
Angle G=57°
Angle H=58°
N=25000, p=0.001, np=25000*0.001=25 >10, so the normal approximation should apply.
fewer than 20 => 0,1,2,3...19
Applying the continuity correction, we have X<19.5.
μ=np=25
σ²=npq=25000*.001*.999=24.975 =>
σ=√(24.975)=4.9975
Z(X<19.5)=(19.5-25)/4.9975=-1.100550
P(X<19.5)=P(Z<-1.10055)=0.1355463 [from normal probability table, left tail]
Hence normal approximation to probability that fewer than 20 cars will be stolen is 0.1355.
[actual value by binomial distribution is 0.133450. approximation is quite close]
