Question

The National Center for Health Statistics estimates that 16.9 percent of U.S. children and adolescents aged 2 to 19 were obese in 2009-2010. Assume that this obesity rate holds true today. If you were to randomly select 18 U.S. children or adolescents, find each of the following: Notei: carry at least 6 digit precision for any intermediate calculations then round your answer to 4 decimal places Note2: Any value that is less than 0.0001, (1 x 10-), can be rounded to O A) The probability that at most 2 people are obese is: B) The probability that exactly 5 people are obese is: C) The probability that none of the people are obese is: D) The probability that at least 2 people in the sample will be obese is:

Answer 1

a)

Here, n = 18, p = 0.169, (1 - p) = 0.831 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 2).
P(X <= 2) = (18C0 * 0.169^0 * 0.831^18) + (18C1 * 0.169^1 * 0.831^17) + (18C2 * 0.169^2 * 0.831^16)
P(X <= 2) = 0.0357 + 0.1307 + 0.226
P(X <= 2) = 0.3924

b)

Here, n = 18, p = 0.169, (1 - p) = 0.831 and x = 5
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 5)
P(X = 5) = 18C5 * 0.169^5 * 0.831^13
P(X = 5) = 0.1064
0

c)

Here, n = 18, p = 0.169, (1 - p) = 0.831 and x = 0
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 0)
P(X = 0) = 18C0 * 0.169^0 * 0.831^18
P(X = 0) = 0.0357

d)

Here, n = 18, p = 0.169, (1 - p) = 0.831 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 1).
P(X <= 1) = (18C0 * 0.169^0 * 0.831^18) + (18C1 * 0.169^1 * 0.831^17)
P(X <= 1) = 0.0357 + 0.1307
P(X <= 1) = 0.1664

P(x> =2) = 1- P(x< =1)
=1 - 0.1664
= 0.8336