Compose a Word document that answers the following questions

Compose a Word document that answers the following questions:

One of the goals of the Obama administration is to ensure all Americans have health insurance. A survey to determine how many Americans have health insurance is an example of (____).

Use the binomial coefficient to determine the number of ways out of a hospital staff of 5 nurses, 2 nurses can be chosen to service the maternity ward.

In a clinical trial, 10 subjects were to be divided equally between the experimental drug and the placebo. How many ways can they be assigned?

Xavier Memorial Hospital investigated the possible ways of defining heart disease in a population. What is the proportion of females with heart disease?

Females n1= 3584

Males n2= 3831

Sample proportion = 43 females

Sample proportion = 17 males

Using the data in the question above, what is the mean of the population when the probability of a woman developing heart disease is 0.5 and that of a man developing heart disease is 0.25?

Solution

We are given that, one of the goals of the Obama administration is to ensure all Americans have health insurance.

a)   A survey to determine how many Americans have health insurance is an example of Binomial distribution with parameter n = number of Americans have health insurance with probability of success is 0.5.

success = Americans who have health insurance.

failuare = Americans who does not have health insurance

b) Use the binomial coefficient to determine the number of ways out of a hospital staff of 5 nurses, 2 nurses can be chosen to service the maternity ward.

binomial coefficient = (n C x) ( C is used for combination)

where, n = number of trials = 5

x = number to be chosen = 2

binomial coefficient = (5 C 2) = 5! / 2!*3!

= 5*4*3*2*1 /(2*1)*(3*2*1)

=120 / 12 =10

c) In a clinical trial, 10 subjects were to be divided equally between the experimental drug and the placebo. How many ways can they be assigned?

Here total number of subjects are 10.

They are equally divided into the two drugs as experimental drug and placebo.

There are only two treatments experimental drug and placebo.

So in (10 C 2) ways the subjects will be assigned.

i.e. in 45 ways the subjects will be assigned.

d) Xavier Memorial Hospital investigated the possible ways of defining heart disease in a population. What is the proportion of females with heart disease?

GIven values are,

Females n1= 3584

Males n2= 3831

Sample proportion = 43 females

Sample proportion = 17 males

Proportion of females with heart disease,

p = number of females in sample / total number of females

= 43 / 3584

= 0.012

e) Using the data in the question above, what is the mean of the population when the probability of a woman developing heart disease is 0.5 and that of a man developing heart disease is 0.25?

We have given that ,

P(woman developing heart disease) = 0.5

P(man developing heart disease ) = 0.25

and the corresponding x-values are 43 and 17.

x 43 17

p(x) 0.5 0.25

E(x) = x*p(x) = 43(0.5) + 17(0.25) = 25.75