Question

Refer to the accompanying technology display. The probabilities were obtained by entering the values of n equals 5 and p equals 0.797. In a clinical test of a​ drug, 79.7​% of the subjects treated with 10 mg of the drug experienced headaches. In each​ case, assume that 5 subjects are randomly selected and treated with 10 mg of the drug. Find the probability that at least four of the subjects experience headaches. Is it unusual to have fewer than four subjects experience​ headaches?

The probability that at least four of the subjects experience headaches is?

Answer 1

Here, we use Binomial distribution

Probability distribution for a binomial random variable is :

where,

n = Number of trials

x = Number of success

p = Probability of success

In our case,

n = 5

p = 0.797

Probability that at least four of the subjects experience headaches = P(X 4)

Now,

Similarly,

So,

Hence,

Probability that at least four of the subjects experience headaches = 0.7311

Now,

Probability that  fewer than four subjects experience​ headaches = 1 - Probability that at least four of the subjects experience headaches

= 1 - 0.7311 = 0.2689

Since, the probability is not so small , we can say that it is not unusual to have fewer than four subjects experience​ headaches.