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ValentinkaMS [17]
3 years ago
15

Suppose in the University of Manitoba, 40% of the students live in apartments. If 600 students are randomly selected, then the a

pproximate probability that the number of them living in apartments will be between 200 and 400 is:(A) .9267(B) .9996(C) .9799(D) .9854(E) .987
Mathematics
1 answer:
just olya [345]3 years ago
6 0

Answer:

P(200\leq X\leq 400)=P(\frac{200-240}{12}\leq \frac{X-\mu}{\sigma}\leq \frac{400-240}{12})=P(-3.33\leq Z \leq 13.33)

=P(Z

So then the correct answer would be:

B) .9996

Step-by-step explanation:

The exact way to solve this problem is using the binomial distribution, assuming that our random variable of interest is "number of students living in apartments" represented by X and X \sim Bin(n=600, p =0.4)

And we want this probability:

P(200 \leq X \leq 400) [tex]In order to find this probability we can use the foloowing excel code:"=BINOM.DIST(400,600,0.4,TRUE)-BINOM.DIST(199,600,0.4,TRUE)"And we got:[tex] P(200 \leq X \leq 400) =0.999675[tex]But for this case the problem says that we need to approximate, so then we can use the normal approximation to the normal distribution. We need to check the conditions in order to use the normal approximation.
[tex]np=600*0.4=240\geq 10

n(1-p)=600*(1-0.4)=360 \geq 10

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

E(X)=np=600*0.4=240

\sigma=\sqrt{np(1-p)}=\sqrt{600*0.4(1-0.4)}=12

And then X \sim N (\mu = 240, \sigma= 12)

And we are interested on the following probability:

P(200\leq X\leq 400)=P(\frac{200-240}{12}\leq \frac{X-\mu}{\sigma}\leq \frac{400-240}{12})=P(-3.33\leq Z \leq 13.33)

=P(Z

So then the correct answer would be:

B) .9996

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I don't understand all three. What am I supposed to do and what is the answer?
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Answer:

Step-by-step explanation:

The Domain means all possible values that x can be.

The range is the outcomes you get when you plug in the domain.

For each function, choose values for x.

Then solve

The outcome you get is f(x)

F(X) is an easier way of saying y,

If its easier this way, in terms of y, the equations would be y=-4x, y=x+6, and y=3x+2. You would solve these as you solve linear equations!

Ordered pair of [x,f(x)]

Lets Start!

#1

x | -4x | f(x)  

Lets use the values -2, -1, 0, 1, and 2 for x.

-2 | -4(-2) | 8  (-2,8)

-1 | -4(-1) | 4  (-1,4)

0 | -4(0) | 0  (0,0)

1 | -4(1) | -4  (1,-4)

2 | -4(2) | -8  (2,-8)

Domain we have right now- {-2,-1,0,1,2}

Range we have right now- {8,4,0,-4,-8}

Domain and Range of entire function- All real numbers

#2

x | x+6 | f(x)

Lets use the values -2, -1, 0, 1, and 2 for x.

-2 | -2 + 6 | 4

-1 | -1 + 6 | 5

0 | 0 + 6 | 6

1 | 1 + 6 | 7

2 | 2 + 6 | 8

Domain we have right now- {-2,-1,0,1,2}

Range we have right now- {4,5,6,7,8}

Domain and Range of entire function- All real numbers

#3

x | 3x + 2 | f(x)

-2 | 3(-2) + 2 | 4

-1 | 3(-1) + 2 | -1

0 | 3(0) + 2 | 2

1 | 3(1) + 2 | 5

2 | 3(2) + 2 | 8

Domain we have right now- {-2,-1,0,1,2}

Range we have right now- {4,-1,2,5,8}

Domain and Range of entire function- All real numbers

Hope i helped, Brainliest would be appreciated.

Have a nice day!

   -Aadi x

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