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2 years ago

Let x be a binomial random variable with n = 15 and p= .5. Using the exact

Mathematics

1 answer:

alexandr1967 [171]2 years ago

7 0

Answer: Choice C) 0.6964; 0.6972

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Work Shown:

n = 15

p = 0.5

q = 1-p = 1-0.5 = 0.5

P(k) = (n C k)*(p)^k*(q)^(n-k)

P(k) = (15 C k)*(0.5)^k*(0.5)^(15-k)

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If you plug in k = 7, then we get,

P(k) = (15 C k)*(0.5)^k*(0.5)^(15-k)

P(7) = (15 C 7)*(0.5)^7*(0.5)^(15-7)

P(7) = 6435*(0.5)^7*(0.5)^8

P(7) = 0.1964

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Repeat for k = 8 all the way through k = 15. You could do this by hand, but I recommend using a spreadsheet to make things go much quicker.

Once you determine those values, add them up and you should get 0.6964 which is the binomial probability we want.

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As for the normal approximation, you'll need to compute the mu and sigma to get

mu = n*p = 15*0.5 = 7.5
sigma = sqrt(n*p*q) = sqrt(15*0.5*0.5) = 1.93649 which is approximate.

The normal distribution will have those parameters.

Since we're using a continuity correction, we need to bump the x = 6 up to x = 6.5, since we want to be larger than 6

Let's find the z score

z = (x - mu)/sigma

z = (6.5 - 7.5)/(1.93649)

z = -0.516398

Now use a Z table or a calculator to determine that P(Z > -0.516398) = 0.6972 approximately. If you're using a TI calculator, then you'll use the normalCDF function. If you're using excel, then you would use the NormDist function (make sure to turn the cumulative flag to "true"). Alternatively, you can search out free z calculators to get the job done.

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Simplify the expression (x^3- 5x^2 + 7x - 12) ÷ (x – 4) using long division

Kisachek [45]

Answer:

${x}^{2} - x + 3$

Step-by-step explanation:

Instead, since the divisor is in the form of $x - c$ , use what is called Synthetic Division. Remember, in this formula, $-c$ gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

4| 1 −5 7 −12

↓ 4 −4 12

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1 −1 3 0 → ${x}^{2} - x + 3$

You start by placing the $c$ in the top left corner, then list all the coefficients of your dividend [x³ - 5x² + 7x - 12]. You bring down the original term closest to $c$ then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an ${x}^{2}$ , the −1 [ $x$ ] follows right behind it, and bringing up the rear, comes the 3, giving you the quotient of ${x}^{2} - x + 3$ .

I am joyous to assist you anytime.

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3 years ago

PLEASE SOMEONE HELP ME

Julli [10]

Answer:

The answer is 5 times

Step-by-step explanation:

First, we need to read the change in price in 2000 and 2007, from the graph.

So, the change in price in 2000 was $0.14 and in 2007 it was $0.71.

Now, we do the same thing we always do when comparing two values - we divide them. So:

0.71 / 0.14 = 5.07

Of course, we could multiply these values with 100, in order to avoid decimal numbers. Then we would get:

71 / 14 = 5.07

We could also divide this in the form of fractions:

71/100 / 14/100 = 5.07

There are several ways we could divide rational numbers, but the result will always be the same.

Change in price in 2007 was around 5 times greater than the change in 2000.

I hope this helps!!;-)

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3 years ago

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Scilla [17]

Answer:

$\checkmark \text{B. The area of the circle is } 729\pi,\\\checkmark \text{D. The arc length of the sector is } 12\pi$

Step-by-step explanation:

Area of a circle with radius $r$ : $r^2\pi$

Circumference of a sector with radius $r$ : $2r\pi$

Area of sector with angle $\theta$ : $r^2\pi\cdot \frac{\theta}{360}$ .

Arc length of sector with angle $\theta$ : $2r\pi\cdot \frac{\theta}{360}$

Using these equations, we get the following information:

Area of circle: $27^2\pi=729\pi$

Circumference of a circle: $2\cdot 27\cdot \pi=54\pi$

Area of sector: $27^2\pi\cdot \frac{80}{360}=162\pi$

Arc length of sector: $2\cdot 27\cdot \pi \cdot \frac{80}{360}=12\pi$

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2 years ago

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Butoxors [25]

Answer:

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3 years ago

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lisov135 [29]

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3 years ago