Question

Refer to the accompanying technology display. The probabilities in the display were obtained using the values of n equals 5 and p equals 0.759. In a clinical test of a​ drug, 75.9​% 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 more than one subject experiences headaches. Is it reasonable to expect that more than one subject will experience​ headaches?

0 0.0008

1. 0.0128

2. 0.0806

3. 0.2540

4. 0.3999

5. 0.2519

The probability that more than one subject experiences headaches is ________ ?

The probability that more than one subject experiences headaches is Is it reasonable to expect that more than one subject will experience headaches?

Yes: because the event that the number of subjects that experience headaches is less than or equal to one is not unlikely. No, because the event that the number of subjects that experience headaches is less than or equal to one is not unlikely. Yes: because the event that the number of subjects that experience headaches is less than or equal to one is unlikely. No, because the event that the number of subjects that experience headaches is less than or equal to one is unlikely.

Answer 1

Answer: The probability that more than one subject experiences headaches is 0.9864

Solution: The cumulative probability distribution function for binomial is defined as,

where,

The probability that more than one subject experiences headaches is,

Given:

X	P(X=x)
0	0.0008
1	0.0128
2	0.0806
3	0.2540
4	0.3999
5	0.2519

From the table,

or the probability can be calculated by this way,

Answer: Yes: because the event that the number of subjects that experience headaches is less than or equal to one is unlikely.

Explanation: From the probability we can see that the probability subject that experience headaches is less than or equal to one = 0.0136 which is unlikely.