The researchers at KT Pharmaceutical Company have developed an experimental drug
ID: 3245807 • Letter: T
Question
The researchers at KT Pharmaceutical Company have developed an experimental drug for treating a disease in cats. The drug needs to be tested to see if it is effective for treating this disease. It is known that about 3 in 500 cats have the disease. With the assistance of a local veterinarian, 305 cats will be randomly sampled for the drug study. Let C be the number of cats in the sample with the disease.
a) Define C in terms of the story and name the distribution, parameter(s), and support.
b) What is the expected number of cats in the sample that have the disease?
c) Set up an equation to find the probability that 2 or 3 cats in the sample have the disease. Fill in the relevant
values in the equation, but do NOT solve it.
d) What is a good approximation for C and what are its parameters? Show that the criteria are met in order to
use this approximation.
e) What is the approximate probability that 2 or 3 cats in the sample have the disease?
Explanation / Answer
(a) C has the binomial distribution, with parameter n = 305 and p = 3/500 = 0.006.
(b) Expected number of cats in the sample = 305 * (3/500) = 1.83
(c) Pr(C =2) = 305C2 (0.006)2 (0.994)303
Pr(C =3) = 305C3 (0.006)3 (0.994)302
(d) A good approximation for C would be poisson distribution with parameter lembda = 1.83 cats
criteria are
(a) Sample size is quite large.
(b) Probability of success is very low.
(e) Possion probability Pr(C =2) = e-2 (1.83)2 /2!= 0.2686
Pr(C =3) = e-3 (1.83)3 /3! = 0.1638