Question

2. Identify if the distribution is binomial or not. If it is binomial, identify n and p.

(a) There are 5 people waiting to see the doctor. There is an equal chance that the doctor will see the next patient within seven minutes. What is the probability the doctor sees one of the waiting patients within the next minute?

(b) Based on past data, 85% of students attend graduation. Twenty-two students are randomly selected. What is the probability that at least 18 will attend graduation?

(c) Patients at two clinics are participating in a study. Clinic A has 35 patients. Clinic B has 30 patients. If 10 patients are chosen at random, what is the probability that 6 will be from Clinic A.

(d) The prevalence of malaria in Nigeria is 62%. What is the probability that you will need to select at least 6 people in order to find one that has malaria?

(e) The sensitivity of a pregnancy test is 98%. If 10 pregnant women are test, what is the probability that 8 or less will test positive for being pregnant?

Answer 1

(a)

This is not a binomial distrbution

Since the probability distribution describes the time between the events. This will consider as Poisson process rather than binomial.

(b)

This is a binomial distribution.

Since the question is for 18 number of success in 22 independent experiments with each outcome has probability of success = 0.85. This is a binomial distribution.

n = 22

p = 0.85

(c)

This is a binomial distribution

Since there are two possible outcome (selecting Clinic A or Clinic B) in 10 independent experiments with each probability of success (selecting clinic A is 35/65) and probability of failure (selecting clinic B is 30/65), this is a binomial distribution.

n = 10

p = 35/65=7/13

(d)

This is not a binomial distribution.

Since the question is asking for the probability for the number of success untill first success occure, this is a geometric distribution.

(e)

This is a binomial distribution

Since there are two possible outcome (positive or negative) in 10 independent experiments with each probability of success (p=0.98) and probability of failure (p=0.02), this is a binomial distribution.

n = 8

p = 0.98