Question

approximately 2% of the nation's children (about 1.7 million) have a parent who is in jail or prison. Let X be the number of children that have an incarcerated parent from a random sample of 100 children.
a) verify that this is a binomial setting and write it in notation.
b) Describe what P(X=0) means in content.
c) Find P(X=0) and P(X=1).
d) What is the probability that two or more of the children have a parent in jail or prison?

Answer 1

Do you know the conditions required for a binomial distribution?

Answer 2

It has to equal to 1

Answer 3

a) P=0.02
N=100

Answer 4

(a)
The following conditions must be met for a binomial distribution to apply:
1.The number in the sample must be fixed. n = 100 in this case.
2. Each trial must have only two possible outcomes. In this case either a parent is incarcerated or is not.
3. The probability of success on any one trial equals a value p which is constant throughout the trials. In this case p = 0.02.
4. The trial are independent of one another.

Al the above conditions are met, so we can write:
X ~ Bin(100, 0.02)

Answer 5

(b)
Do you know what P(X=0) means in the content of the question?

Answer 6

P(X=0) means the probability that none of the children in the sample of 100 has an incarcerated parent.
(c)
\[P(X=0)=(1-0.02)^{100}=you\ can\ calculate\]
\[P(X=1)=\left(\begin{matrix}100 \\ 1\end{matrix}\right)0.02^{1} \times0.98^{99}=100\times0.02\times0.98^{99}=you\ can\ calculate\]

Answer 7

ThaThanks

Answer 8

You're welcome :)

Answer 9

can you help with two more?

Answer 10

Sorry, I have to log out now. Please post as new questions.