The rate of births by Cesarean section Csection in the Unite

The rate of births by Cesarean section (C-section) in the United States is 32%. You are interested in gathering survey information from new mothers in your city about their hospital experiences. Assume that the type of birth is independent among the new mothers.

a) A specific set of questions is geared towards those new mothers whose baby was born by C-section. What is the probability that the first new mother who delivered her baby by C-section is the fourth one you interviewed? What distribution and parameter(s) are you using? (5 points)

b) What is the probability that you must interview at least 4 new mothers to find the first one who delivered her baby via C-section? (3 points)

c) In order to gather all the information you need for your survey, you must get responses from 5 new mothers who did NOT deliver their babies by C-section. What is the probability that you interviewed 8 new mothers to get these needed responses? What distribution and parameter(s) are you using? (5 points)

d) What is the standard deviation of the number of new mothers interviewed in order to find 5 who did not deliver their babies by C-section? (3 points)

Solution

a)

Prob for 4th mother to be the first Caeserean section

= Prob for first 3 normal and 4th C

= 0.68³(0.32)

= 0.1006

c)

= rt of 0.32(0.68)n