Malaria is a debilitating and potentially deadly parasitic infection. It can be

Question

Malaria is a debilitating and potentially deadly parasitic infection. It can be cured and is mostly preventable with community health precautions but many developing countries lack the necessary resources. The West African Country of Guinea has a high rate of malaria, with 70% of its population infected.

A physician from “Doctors without Borders” sees 4 patients in a given hour. Assume the patient visits are independent.

Let X be the count of patients who are infected with malaria among the 4 patients seen in any random one hour.

a) What is the probability of the Bernoulli event of “having malaria”? ..........

b) What is the number of trials in the situation above? .........

c) What is the question that can be answered by a Binomial distribution?

d) State the probability distribution of X above (type and its parameters):

X~ ................

e) State the formula for P(X=x) and define all terms used:

STA1010 Statistical Methods for Science

Evaluate the probability distribution of X:

x

Pr(X=x)

0

1

2

3

4

Check your distribution... does it add to 1? (more questions over page)

f) Draw a probability histogram for the distribution of X (remember that these are discrete probabilities).

g) Find the probability that the doctor will see “at most” one patient with malaria in any hour (use correct notation for Probability involved)

h) Find the probability that there are 2 or more cases of malaria in any hour (use correct notation for Probability involved).

x

Pr(X=x)

0

1

2

3

4

Explanation / Answer

a)Here, the probability of the Bernoulli event of “having malaria” is p = 0.7

b)The number of trials in the situation above is n = 4.

c)Suppose the event of having malaria is considered to be a success with probability p = 0.7 and the event of not having malaria is considered to be a failure with probability q = 1-p = 0.3.
The question that can be answered is like what is the probability that for number of trials n = 4, atleast 2 successes can be observed or 3 successes is observed, etc.

d)Here, X is a random variable.
X~Binomial(n=4,p=0.7)

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