Answer to Question #193137 in Statistics and Probability for Abel

Question

a company makes raincoat and claim that 95%of its coats will pass a standard waterproof test. fifty coats are chosen at random from the production line, assuming that the firm's claim is correct, find a) the average number of coats that would be expected to fail; b) the probability that more than one coat will fall the test

Answer 1

Total number of coats=50

According to company's claim , No. of coats which pass the standard waterproof test$=\dfrac{95}{10}\times 50=47.5$

Probability of coats passing waterproof test $= \dfrac{47.5}{50}=0.95$

Probability of coats fail the test $p=1-0.95=0.05$

(a) The Average number of coats that would be expected to fail

$E=np=50\times 0.05=2.5$

(b) The probability that more than one coat will fall the test

$P(X>1)=1-P(X\le 1)=1-[P(x=0)+P(X=1)]$

$=1-[^{50}C_0(0.05)^0(0.95)^{50}+^{50}C_1(0.05)^1(0.95)^{49}]\\ =1-[0.0769+0.202]\\ =1-0.2789\\=0.7211$