Question

# Answers as percentages with one decimal place e.g. 20.7%

1.   Binomial Distributions: The three-year survival rate for heart transplantation is 75%. A hospital has performed 140 transplants from 2002 through 2007 and has conducted a survey to determine how many of their patients were alive at the end of their third year, calculate the following probabilities"

A.     What is the probability that 105 patients (or 75%) or more survived?         ______

B.     What is the probability that 112 patients (or 80%) or more survived?         ______

C.     What is the probability that 133 patients (or 95%) or more survived?         ______

D.     What is the probability that 94 or less patients (or 67%) survived?             ______

2.    Poisson Distributions: Nosocomial infections occur at an incidence rate of 5 infections per 1,000 patient-days.  Based on the 35 million patients admitted in the United States, the incidence of HAIs is more than 2 million cases per year. HAIs result in 26,250 deaths and expenditures in excess of \$4.5 billion (Wenzel R, Edmond, The Impact of Hospital Acquired Blood Stream Infections. Emerg Inf Dis. Mar-Apr 2001; 7(174). If a hospital has 2,000 patient days per month, calculate the following probabilities:

a. What is the probability that the hospital will see exactly five infections?     ______

b. What is the probability that the hospital will see eight or fewer infections?  ______

c. What is the probability that the hospital will see 12 or more infections?      ______

d. What is the probability that the hospital will see 16 or more infections?      ______  