Question

It is known that 10% of bolts manufactured by a factory are defective. If a random sample of 100 bolts is chosen at random from a day's production, construct the sampling distribution of (1) the number of defective bolts, (2) the proportion of defective bolts.

Answer 1

1) N=n*p=100*0.1=10

2) sampling distribution of a sample proportion

$\mu_\rho=p=0.1,$

$\sigma_\rho=\sqrt{\frac{p(1-p)}{n}}$ =0.03.