1. The prevalence of diabetes in Nevada is 10%. Suppose we take a simple random

Question

1. The prevalence of diabetes in Nevada is 10%. Suppose we take a simple random sample of 15 people from Nevada. Let X represent the number of individuals in the sample with diabetes. a) Use notation and appropriate values to describe the distribution X. (1 point) b) What is the probability of seeing no cases in the sample? (2 points) c) What is the probability of seeing one case? (2 points) d) What is the probability of seeing one or no cases? (2 points) e) What is the probability of at least two cases? (2 points)

Explanation / Answer

Solution:
We will use bionomial distribution in this case
Given in the question:
n=no. of observations = 15
= probability of an event of interest = 0.10
Solution(b)
P(X=0 | n=15, = 0.1) = 15C0 *(0.1)^0 * (0.9^15) = 1*1*0.20589 = 0.20589
So there is 20.59% of chances that there are no cases in the sample
Solution(c)
P(X=1 | n=15, = 0.1) = 15C1 *(0.1)^1 * (0.9^14) = 15*0.1*0.22876 = 0.34314
So there is 34.314% chances that there are one case
Solution(d)
P(X=0 or 1 n=15, = 0.1) = P(X=0) + P(X=1) = 0.20589 + 0.34314 = 0.54903
So there are 54.903% chances of seeing one or no cases.
Solution(e)
P(X>=2 | n=15, = 0.1) =1- ( P(X=0) + P(X=1)) = 1-0.54903 = 0.45097
So there is 45.097% chances of atleast two cases.

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