A biotechnology company produced 196 doses of somatropin, including 9 which were defective. Quality control test 10 samples at random, and rejects the batch if any of the random samples are found defective. What is the probability that the batch gets rejected?

Answer: 0.3756Step-by-step explanation:Given : A biotechnology company produced 196 doses of somatropin, including 9 which were defective. Proportion of defective doses of somatropin : [tex]p=\dfrac{9}{196}=0.0459183673469\approx0.046[/tex]Using binomial probability formula,[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]If Quality control test 10 samples at random, and rejects the batch if any of the random samples are found defective. Then, the probability that the batch gets rejected will be :-[tex]P(x\geq1)=1-P(x=0)\\\\=1-^{10}C_0(0.046)^0(1-0.046)^{10}\\\\=1-(1-0.046)^{10}\\\\=1-0.624429981287\\\\=0.375570018713\approx0.3756[/tex]Hence, the probability that the batch gets rejected = 0.3756