A recent study reported that the prevalence of hyperlipidemia (defined as total cholesterol over 200) is 30% in children 2-6 years of age. If 12 children are analyzed. Required:
a. What is the probability that at least 3 are hyperlipidemic?
b. What is the probability that exactly 3 are hyperlipidemic?
c. How many would be expected to meet the criteria for hyperlipidemia?

(a) 0.7472

(b) 0.2397

(c) 3.6

Step-by-step explanation:

Let X denote the number of children who are hyperlipidemic.

The proportion of children who are hyperlipidemic is, p = 0.30.

A random sample of n = 12 children are analyzed.

Every child is independent of the others to be expected to meet the criteria for hyperlipidemia.

The random variable X follows a binomial distribution with parameters n = 12 and p = 0.30.

(a)

Compute the probability that at least 3 are hyperlipidemic as follows:

Thus, the probability that at least 3 are hyperlipidemic is 0.7472.

(b)

Compute the probability that exactly 3 are hyperlipidemic as follows:

Thus, the probability that exactly 3 are hyperlipidemic is 0.2397.

(c)

Compute the expected number of children who would meet the criteria for hyperlipidemia as follows:

Thus, 3.6 children would be expected to meet the criteria for hyperlipidemia.

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.