Question

The probability that a patient recovers from a stomach disease is 0.6. Suppose 20 people are known to have contracted this disease. (Round your answers to three decimal places.)

(a)

What is the probability that exactly 14 recover?

(b)

What is the probability that at least 11 recover?

(c)

What is the probability that at least 14 but not more than 19 recover?

(d)

What is the probability that at most 16 recover?

You may need to use the appropriate appendix table or technology to answer this question.

Answer 1

The number of people who recover out of 20 patients is modelled as:

a) The required probability here is computed using the binomial tables as:

For n = 20, x = 14 and p = 0.6

P(X = 14) = 0.124

Therefore 0.124 is the required probability here.

b) P(X >= 11) = 1 - P(X <= 10)

From the cumulative probability distribution tables for binomial distribution

For x = 10, n = 20 and p = 0.6, we get:

P(x <= 10) = 0.245

Therefore P(x >= 11) = 1 - 0.245 = 0.755

Therefore 0.755 is the required probability here.

c) Again using the above tables as:

P( 14 <= X <= 19) = P(X <= 19) - P(X <= 13) = 1 - 0.750 = 0.250

Therefore 0.250 is the required probability here.

d) P( x<= 16) = 0.984 ( directly from the table above )

Therefore 0.984 is the required probability here.