Question

There is a probability of 20% that a milk container is underweight throughout of packaging line. Suppose milk containers are shipped to retail outlets in boxes of 10 containers. What is the probability that at least nine milk containers in a box are properly filled?

Answer 1

Answer: 0.3758

Step-by-step explanation:

Given : The  probability that a milk container is underweight throughout of packaging line: $p = 0.20$

The number of containers : n= 10

The formula binomial distribution formula :-

$^nC_rp^{n-r}(1-p)^r$

The probability that at least nine milk containers in a box are properly filled is given by :-

$P(X\geq9)=P(9)+P(10)\\\\=^{10}C_9(0.2)^{10-9}(1-0.20)^9+^{10}C_{10}(0.2)^{10-10}(1-0.2)^{10}\\=10(0.2)(0.8)^9+(1)(0.8)^{10}\\=0.3758096384\approx0.3758$