Exercise 8 Page 827

We are considering a medical study testing a new cough medicine.

Experimental Probability

We first want to find the experimental probability that the medicine is effective. We will use the results of the study and compare the number of times the event we are interested in occurs to the number of times the experiment is done. P = Times the event occurs/Times the experiment is doneIn our case, 4250 people try the new medicine, so the experiment is conducted 4250 times. The event occurs when the medicine is effective. Since 3982 people found the medicine to be effective, the event occurs 3982 times. We have enough information to calculate the desired probability.

P(effective) = Times the event occurs/Times the experiment is done

SubstituteValues

Substitute values

P(effective) = 3982/4250

CalcQuot

Calculate quotient

P(effective) = 0.936941...

RoundDec

Round to 3 decimal place(s)

P(effective) ≈ 0.937

The probability that the medicine is effective is about 0.937, or about 93.7 %.

Prediction

Next, we want to find the approximate number of people out of a group of 9000 for whom the medicine will be effective. To do so, let's denote the number approximate number of people for whom the medicine will be effective as e and the total number of people in the group as t. We will consider the following formula. e = P(effective) * t There are 9000 people in the group, so we will substitute 9000 for t. The probability that the medicine will actually be effective is the probability obtained earlier. This means that we can substitute 0.937 for P(effective).

e = P(effective) * t

SubstituteII

P(effective)= 0.937, t= 9000

e = 0.937 * 9000

Multiply

Multiply

e = 8433

The approximate number of people for whom the medicine will be effective is about 8433.