Question

You may need to use the appropriate appendix table or technology to answer this question. A center for medical services reported that there were 295,000 appeals for hospitalization and other services. For this group, 55% of first-round appeals were successful. Suppose 10 first-round appeals have just been received by a Medicare appeals office. (Round your answers to four decimal places.) (a) Compute the probability that none of the appeals will be successful. (b) Compute the probability that exactly one of the appeals will be successful. (c) What is the probability that at least two of the appeals will be successful? (d) What is the probability that more than half of the appeals will be successful?

Answer 1

Let X is a random variable shows the number of  first-round appeals that were successful out of 10. Here X has binomial distribution with parameters as follows:

n=10 and p=0.55

(a)

The probability that none of the appeals will be successful is

10 (0.55)(1 -0.55)10- P(X 0) 0.0003

(b)

The probability that exactly one of the appeals will be successful is

10 (0.55)'(1 -0.55)10 P(X 1) 1 0.0042

(c)

The probability that at least two of the appeals will be successful is

P(X 2) 1 P(X 0)- P(X= 1) 1-0.0003 0.0042 0.9955

(d)

The  probability that more than half, that is more than 5,  of the appeals will be successful is

10 10 (0.55)( 0.55)10 0.5044 P(X >5) エ=6