Ask question

Ask question

All categories

2 years ago

14

In the exercise, X is a binomial variable with n = 9 and p = 0.3. Compute the given probability. Check your answer using technol

ogy. HINT [See Example 2.] (Round your answer to five decimal places.) P(X = 5)

1 answer:

Sati [7]2 years ago

4 0

Answer: The required probability is 0.07351.

Step-by-step explanation: Given that X is a binomial variable with n = 9 and p = 0.3.

We are given to compute the probability P(X = 5) and round the answer to five decimal places.

We know that

the binomial distribution formula for P(X = r) with n number of trials is given by

$P(X=r)=^nC_rp^rq^{n-r},~~\textup{where }q=1-p.$

According to the given information, we have

n = 9, p = 0.3 and q = 1 - p = 1 - 0.3 = 0.7.

Therefore, we get

$P(X=5)\\\\=^9C_5(0.3)^5(0.7)^{9-5}\\\\\\=\dfrac{9!}{5!(9-5)!}(0.3)^5(0.7)^4\\\\\\=\dfrac{9\times8\times7\times6\times5!}{5!\times4\times3\times2\times1}\times0.00273\times.2401\\\\=126\times0.000583443\\\\=0.073513818.$

Rounding to five decimal places, we get

P(X=5) = 0.07351.

Thus, the required probability is 0.07351.

You might be interested in

One fifth of the sum of 9 and h

8090 [49]

Answer:

= (9 + h) /5

Step-by-step explanation:

One fifth means 1/5

Sum of 9 and h = (9 +h)

One fifth of sum of 9 and h = 1/5 x (9 + h)

= (9 + h) /5

I hope this was helpful, Please mark as brainliest

8 0

3 years ago

Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

2 years ago

Which is a counterexample for conditional statement shown? If two distinct points are graphed on a coordinate plane, then the li

Ilya [14]

Answer:

It's A: The points have the same x-coordinate value.

8 0

2 years ago

Point B, located at (-4, -7), is reflected over the y-axis. What are the coordinates of B'?

strojnjashka [21]

(-4,7) answer A
if u reflect it over y axis

3 0

2 years ago

Read 2 more answers

the speed that a tsunami can travel is modeled by the equation mc025-1.jpg , where s is the speed in kilometers per hour and d i

Flura [38]

The answer is a.0.32 km.

The speed that a tsunami can travel is modeled by the equation is s = 356√d.

It is given:
s = 200 km/h
d = ?

Now, let's substitute s in the equation and find d:
s = 356√d
200 = 356√d
√d = 200 ÷ 356
√d = 0.562

Now, let's square both sides of the equation:
(√d)² = (0.562)²
d = (0.562)² = 0.316 ≈ 0.32

Therefore, <span> the approximate depth (d) of water for a tsunami traveling at 200 kilometers per hour is 0.32 km.</span>

5 0

2 years ago

Read 2 more answers