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xz_007 [3.2K]
2 years ago
13

Point $(x,y)$ is randomly picked from the rectangular region with vertices at $(0,0),(2009,0),(2009,2010),$ and $(0,2010)$. What

is the probability that $x > 7y$? Express your answer as a common fraction.

Mathematics
2 answers:
Bezzdna [24]2 years ago
6 0

Answer: Probability that x>7y is \frac{287}{4020}

Step-by-step explanation:

Since we have given that

x>7y

And the coordinates are as follows:

(0,0),(2009,0),(2009,2010), and (0,2010)

We need to find the probability that x>7y

So, Required Probability is given by

\frac{\text{Area of triangle}}{\text{ Area of rectangle}}\\\\=\frac{0.5\times 2009\times 287}{2009\times 2010}\\\\=\frac{287}{4020}

Hence, Probability that x>7y is \frac{287}{4020}

pantera1 [17]2 years ago
6 0

Answer:

Hence, the probability is:

\dfrac{287}{4020}

Step-by-step explanation:

We know that probability of an event is defined as:

Probability=(Number of favourable events)/(Total number of events)

The probability that x > 7y is given by:

Here the number of favourable event is equal to the area covered by the triangle ΔABE

Area of triangle ABE= (1/2)×b×h=(1/2)×2009×287=288291.5

and the total outcome is equal to the area of the rectangle (i.e. rectangle ABCD)

Area of rectangle ABCD=2009×2010=4038090

Hence, probability=

\dfrac{288291.5}{4038090}=\dfrac{287}{4020}

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In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students what is the probability tha
zimovet [89]

Answer:

a) The expected value is given by:

E(X) = np = 50*0.4 = 20

and the variance is given by:

Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12

b) P(X>25)= 1-P(X\leq 25)

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

P(X>25)= 1-P(X\leq 25)=0.0573

c) 1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

X \sim N(\mu = 20 , \sigma= 3.464)

d) P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z

e) P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=50, p=0.4)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

The expected value is given by:

E(X) = np = 50*0.4 = 20

and the variance is given by:

Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12

Part b

For this case we want to find this probability:

P(X>25)= 1-P(X\leq 25)

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

P(X>25)= 1-P(X\leq 25)=0.0573

Part c

1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

X \sim N(\mu = 20 , \sigma= 3.464)

Part d

We want this probability:

P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z

Part e

For this case we use the continuity correction and we have this:

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z

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Answer:

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Step-by-step explanation:

4) you’d look at the row from 8:00-8:59.

5) Add the first two rows together (6+2=8), then subtract that by the sum of  the last two rows (9+6=15), which is 7

6) There’s no pattern in the frequency table, and the data points would be plotted differently since it’d be from a range of times, not one set time.

Hope this helped, sorry if I’m wrong on #6 ;)

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