Find the solution set of the inequality 7x−10≥16.

In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal p

skelet666 [1.2K]

Answer:

$\mathbf{P(X=5) =0.0888}$

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

$\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}$

$\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}$

where;

n = 8 and π = 0.36

For x = 5

The probability $\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}$

$\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =0.0887645}$

$\mathbf{P(X=5) =0.0888}$ to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5) $\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})$

${P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +$ $\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )$

P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888

P(x ≤ 5 ) = 0.9707

c. x ≥ 6

The probability of P ( x ≥ 6) = 1 - P( x ≤ 5 )

P ( x ≥ 6) = 1 - 0.9707

P ( x ≥ 6) = 0.0293

4 0

2 years ago

Suppose a city with population 300 comma 000 has been growing at a rate of 3% per year. If this rate continues, find the popul

viktelen [127]

Answer:

The population of this city in 13 years is 440,550.

Step-by-step explanation:

Given:

Suppose a city with population 300, 000 has been growing at a rate of 3% per year.

Now, to find the population of this city in 13 years.

Let the population of this city in 13 years be $A.$

Population ( $P$ ) = 300,000.

Rate per year ( $r$ ) = 3%.

Time ( $t$ ) = 13 years.

Now, we put formula to get the population of the city in 13 years:

$A=P(1+r)^t\\\\A=300,000(1+3\%)^{13}\\\\A=300,000(1+0.03)^{13}\\\\A=300,000(1.03)^{13}\\\\A=300,000\times 1.4685\\\\A=440,550.$

Therefore, the population of this city in 13 years is 440,550.

3 0

2 years ago

Can someone help with 11-15

lozanna [386]

Answer: -4

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

How to convert 2.4 to radical form

DedPeter [7]

To convert 2.4 into a radical you have to write the equation;
2.4=√x; then you square both sides, to get x by itself, resulting in 5.8; and then you have to write; "2.4 in radical form is the square root of 5.8

6 0

3 years ago

Can you give me an answer to this problem? 100m + 60m + ?m<br><br> Pythagorean thereon

laila [671]

Answer:

116.62m

Step-by-step explanation:

$c= \sqrt{a^2+b^2} = \sqrt {100^2+60^2} approx. 116.61904$

5 0

2 years ago