The 2% of the parts produced by a machine are defective. If a random sample of 60 parts is taken, what is the probability that there are between 0 and 2 defective parts?
Hi! I need help with this exercise. I know i have to check first if the sampling distribution of $\hat{p}$ is approximately normal. For that I need that $np \geq 10$ and $n(1-p) \geq 10$.
So, when checking that the first one fail.
$60(0.02) = 1.2 < 10$
So that's mean is not approximately normal? If that is so, what do I do then?
I did this $\sigma_{\hat{p}}=\sqrt{\frac{0.02(1-0.02)}{60}}=0.018074$
Then,
$\hat{p_1}=\frac{0}{60}=0$
$\hat{p_2}=\frac{2}{60}=0.033$
$z_{1}=\frac{0-0.02}{0.018074}=-1.11$
$z_{2}=\frac{0.033-0.02}{0.018074}=0.72$
So the probability,
$P(0<\hat{p}<0.033)=P(-1.11<z<0.72)=P(z<0.72)-P(z<-1.11)=0.7640-0.1342=0.6298$
This is what I have but I'm not sure since $np< 10$