Question

Refer to the accompanying technology display. The probabilities in the display were obtained using the values of n equals n=5 and p equals p=0.732. In a clinical test of a​ drug, 73.2​% of the subjects treated with 10 mg of the drug experienced headaches. In each​ case, assume that 55 subjects are randomly selected and treated with 10 mg of the drug. Find the probability that more than one subject experiences headaches. Is it reasonable to expect that more than one subject will experience​ headaches?
BInomial with n=5 and p= 0.732

X P(X=x)
0 0.0014
1 0.0189
2 0.1031
3 0.2817
4 0.3847
5 0.2102
The probability that more than one subject experiences headaches is

Answer 1

Answer:

• Yes, it is reasonable to expect that more than one subject will experience​ headaches

Explanation:

Notice that where it says "assume that 55 subjects are randomly selected ..." there is a typo. The correct statement is "assume that 5 subjects are randomly selected ..."

You are given the table with the probability distribution, assuming, correctly, the binomial distribution with n = 5 and p = 0.732.

• p = 0.732 is the probability of success (an individual experiences headaches).
• n = 5 is the number of trials (number of subjects in the sample).

The meaning of the table of the distribution probability is:

The probability that 0 subjects experience headaches is 0.0014; the probability that 1 subject experience headaches is 0.0189, and so on.

To answer whether it is reasonable to expect that more than one subject will experience​ headaches, you must find the probability that:

• X = 2 or X = 3 or X = 4 or X = 5

That is:

• P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5).

That is also the complement of P(X = 0) or P(X = 1)

• 1 - P(X = 0) - P(X = 1)

From the table:

• P(X = 0) = 0.0014
• P(X = 1) = 0.0189

Hence:

• 1 - P(X = 0) - P(X = 1) = 1 - 0.0014 - 0.0189 = 0.9797

That is very close to 1; thus, it is highly likely that more than 1 subject will experience headaches.

In conclusion, yes, it is reasonable to expect that more than one subject will experience​ headaches