Question

The equation for the height of a stack of blocks labelled A, B, and C is
h=?+?+?. If the processes that produce the blocks have the following paramters:
Block. μ.           σ
A 10.5 mm 0.4 mm
B 12.0 mm 1.2 mm
C 4.5 mm 0.3 mm
i) Calculate the mean and standard deviation of the height h.
ii) If the distributions of A, B, and C are normal, it follows that h will be normally
distributed too. If this is the case, what is the probability that the stack height will
be greater than 29 mm?

Answer 1

i)

mean of h =E(h)=E(A+B+C) =10.5+12+4.5=27

standard deviation of h =sqrt(Var(A)+Var(B)+Var(C)) =sqrt(0.4^2+1.2^2+0.3^2)=1.3

ii)

for normal distribution z score =(X-μ)/σx

probability =P(X>29)=P(Z>(29-27)/1.3)=P(Z>1.54)=1-P(Z<1.54)=1-0.9382=0.0618