Question

Suppose that the probability that a child living in an urban area in the United States is obese is 20%. If a social worker sees 15 children living in urban areas, answer the following: What is the probability that none are obese

Answer 1

The probability the event that none of them are obese is 0.0352.

Explanation:

Binomial distribution:

A discrete random variable X having to the set {0,1,2,3....,n} as the spectrum, is said to have binomial distribution with parameters n= the number of trial, and p= probability of successes on an individual trial , if the p.m.f of X is given by,

`P(X=x)=\left(\begin{array}{c}n\\x\end{array}\right) p^x(1-p)^(n-x)` for x=0,1,2,...,n

=0 elsewhere.

where 0<p<1 and n an positive integer,

Given that,

The probability of the event that a child living in an urban area in the united state is obese is 20%.

n=Number of children = 15, p= 20%= 0.20.

The probability the event that none of them are obese is

=P(X=0)

`=\left(\begin{array}{c}15\\0\end{array}\right) (0.20)^0(1-0.20)^(15-0)`

=0.0352