Mei is investigating contamination in sets of 12 laboratory samples. She models the number of contaminated samples in a set by X∼B(12,0.10)X\sim B(12,0.10)X∼B(12,0.10).
Using Mei's model, find P(X≥3)P(X \ge 3)P(X≥3).
Mei examines 50 sets. Using the model, find the expected number of sets containing no contaminated samples.
Of the 50 sets, 15 contain no contaminated samples and 6 contain at least 3 contaminated samples. State, with a reason, whether these observations support Mei's model.