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Suppose that a random sample of 10 people are selected for a trial of a vaccine for a childhood disease.

(a) If 40% of the population has had the disease, what is the probability of at least 3 in the sample who have had the disease?

(b) Suppose 80% of the population will develop a rash from the vaccination. What is the probability that 5 or fewer subjects develop a rash?

Use the tabulated values of the Binomial distribution function to answer the questions.

**Table 1:** Table of the binomial cumulative distribution function. The tabulated values are $P[X \le x]$ when X has a binomial distribution with n = 10 and p as given.
x	p=.1	p=.2	p=.3	p=.4	p=.5
0	0.349	0.107	0.028	0.006	0.001
1	0.736	0.376	0.149	0.046	0.011
2	0.930	0.678	0.383	0.167	0.055
3	0.987	0.879	0.650	0.382	0.172
4	0.998	0.967	0.850	0.633	0.377
5	1.000	0.994	0.953	0.834	0.623
6	1.000	0.999	0.989	0.945	0.828
7	1.000	1.000	0.998	0.988	0.945
8	1.000	1.000	1.000	0.998	0.989
9	1.000	1.000	1.000	1.000	0.999
10	1.000	1.000	1.000	1.000	1.000

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Dennis Cox
3/8/2001