Question

The length in cm of components manufactured by a machine come from a normal population with mean 36 standard deviation 2.5. if 5 components are randomly selected from the machine's output. What is the probability at least 2 are are longer than 37.5cm

Answer 1

I found it , if anyone is interested P(X > 37.5) = P((X-35)/2.5 > (37.5-35)/2.5) = P(Z > 1) .

Get P(Z > 1) off standard normal table by 1-P(Z<1)=

Answer 2

1-0.8413=0.1587

Answer 3

Now using the binomial with P(Y>=2)=1-P(Y<2)
n=5 and p=P(Z>1)=0.1587

Answer 4

final answer is 0.1810 , correct me if i am wrong