Mathematics, 20.03.2020 20:58 beaaaaast3

By some estimates, twenty-percent (20%) of Americans have no health insurance. Randomly sample n = 15 Americans. Let X denote the number in the sample with no health insurance. (a) What is the probability that exactly 3 of the 15 sampled have no health insurance? (b) What is the probability that at most 1 of those sampled have no health insurance?

Answers: 1

Show answers

Answers

Answer from: Ey3lean

a) 25.01% probability that exactly 3 of the 15 sampled have no health insurance.

b) 16.71% probability that at most 1 of those sampled have no health insurance

Step-by-step explanation:

For each person in the sample, there are only two possible outcomes. Either they have no health insurance, or they have. The probability of a person having health insurance is independent of any other person. So we use the binomial probability distriution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

By some estimates, twenty-percent (20%) of Americans have no health insurance.

This means that p = 0.2

Randomly sample n = 15 Americans

This means that n = 15 .

(a) What is the probability that exactly 3 of the 15 sampled have no health insurance?

This is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{15,3}.(0.2)^{3}.(0.8)^{12} = 0.2501$

25.01% probability that exactly 3 of the 15 sampled have no health insurance.

(b) What is the probability that at most 1 of those sampled have no health insurance?

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{15,0}.(0.2)^{0}.(0.8)^{15} = 0.0352$

$P(X = 1) = C_{15,1}.(0.2)^{1}.(0.8)^{14} = 0.1319$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0352 + 0.1319 = 0.1671$

16.71% probability that at most 1 of those sampled have no health insurance

Answer from: Quest

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

$\text{simple interest} = \frac{principal\times rate\times time}{100} \\\\\text{simple interest} = \frac{1000\times 4\times 10}{100}=\$400\\\\amount = principal + interest\\amount = 1000 + 400 = \$1400$

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

Answer from: Quest

$a^b=\underbrace{a\cdot a\cdot \ldots \cdot a}_{b}$

a - base

b - exponent

$8^3=\underbrace{8\cdot 8 \cdot 8}_{3}$

so,

the base is 8the exponent is 3the exponent tells you to multiply 8 together three timesthe expanded form is 8*8*8

Another question on Mathematics

Mathematics, 21.06.2019 18:00

What is the location of point g, which partitions the directed line segment from d to f into a 5: 4 ratio? –1 0 2 3

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

Ageologist had two rocks on a scale that weighed 4.6 kilograms together.rock a was 0.5 of the total weight.how much did rock a weigh?

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

Anyone know these questions? i need ,.

Answers: 1

Answer

You know the right answer?

By some estimates, twenty-percent (20%) of Americans have no health insurance. Randomly sample n = 1...

Questions