Arecent study reported that the prevalence of hyperlipidemia (defined as total cholesterol over 200) is 30% in children 2-6 year of age. if 12 children are analyzed:
a. what is the probability that at least 3 are hyperlipidemic?

The probability is 0.74719

Step-by-step explanation:

Let's start defining the random variable X.

X : ''Number of children with hyperlipidemia out of 12 children''

X can be modeled as a binomial random variable.

X ~ Bi (n,p)

Where n is the sample size and p is the ''success probability''.

We defining as a success to find a child that has hyperlipidemia.

The probability function for X is :

Where nCx is the combinatorial number define as :

We are looking for

There is a probability of 0.74719 that at least 3 children are hyperlipidemic.

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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