A biologist plants 10 seeds in each of 200 trays and records how many germinate in each tray. She models the number germinating in a tray by the random variable XXX, where X∼B(10,0.7)X \sim B(10, 0.7)X∼B(10,0.7).
State two conditions needed for the binomial model to be appropriate.
Using the model, find the expected number of trays in which all 10 seeds germinate.
In fact, all 10 seeds germinated in 22 of the 200 trays. Comment on the model in the light of this.
Suggest one reason why a binomial model may not be appropriate for this situation.