1. Based on data from the National Center for Health Statistics, the prevalence

Question

1. Based on data from the National Center for Health Statistics, the prevalence of diabetes among seniors (>65 years old) is 30%. You take out a simple random sample 15 senior adults. Let X represent the number of individuals in the sample with diabetes.

a. Describe the distribution X.

b. What is the probability of seeing no diabetes case in this sample?

c. What is the probability of seeing one diabetes case?

d. What is the probability of seeing one or less diabetes case?

e. What is the probability of seeing at least two diabetes cases?

Explanation / Answer

a)

This is binomial distribution

X ~ Binomial(15,0.30)

b)

Binomial probability distribution is

p(x) = nCx px (1-p)n-x

p( x = 0) = 15C0 0.300 0.7015

= 0.004748

c)

p( X =1 ) =  15C1 0.301 0.7014

= 0.03052

d)

p( x <= 1) = p( x = 0) + p( x = 1)

= 0.004748 + 0.03052

= 0.035268

e)

p( x >=2) = 1 -p( x <=1)

= 1 - 0.035268

= 0.964732

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