there are 3 three questions before this question that i am about to post.

from the previous question i have worked out the following values:

Below is the values of E:

25 items faulty = 78

150 "" "" = 28

250 "" "" = -12

Below are the values of p

25/1000 = 0.025

150/1000 = 0.15

250/1000 = 0.25

You now have 3 values of profit, E (given above.) corresponding to the 3 values of p, the probability that any particular item is faulty.

Take any of those 3 values of p, together with the corresponsing values of E and thus determine E as a linear funtion of P.

Show that the 3rd value of p and the corresponding value of E agree with this linear funtion.

From your linear funtion determine, within the context of this application, the finite rannge of values of p which gives a positive value for E.

Any help on the above question will be highly appreciated thanks in advance.