Several insects are released at a site equidistant from the

Several insects are released at a site equidistant from the P under study and a control substance. If the P has an effect more insects will travel toward it later than toward the control. Otherwise, the insects are equally likely to travel in either direction. Suppose the P under study has no effect so that it is equally likely that an insect will move toward the P or toward the control. Suppose five insects are released.

( P is Pheromone)

b) What is the chance that all five travel toward the P?

c) What is the chance that exactly four travel toward the pheromone?

d? What inference would you make if the event in part c actually occurs? Explain

Solution

here the assumption is that the P under study has no effect. so it is equally likely that an insect will move toward the P or toward the control

so the probability that an insect will move toward the P=probability that an insect will move toward the control=0.5

5 insects are released. the movements of the insects are independent.

let X denote the number of insects move toward P

then X~Bin(5,0.5)

b) the probability that all five travel toward the P

=P[X=5]=⁵C₅0.5⁵=0.03125 [answer]

c)to find the probability that exactly four travel toward the pheromone we need to find

P[X=4]=⁵C₄0.5⁴(1-0.5)¹=0.15625 [answer]

d) if the event in part c actually occurs i.e, if four insects travel toward the pheromone then we have more insects travelling toward P than toward the control. hence P should have an effect on the insects as in the question it is stated that If the P has an effect more insects will travel toward it later than toward the control.

hence the inference is that P has an effect on the insects.