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Paraphin [41]
3 years ago
13

Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. The distrib

ution for the units is given below.X 3 4 5 6 7 8 9 10P(X) 0.1 0.24 0.33 0.17 0.05 0.05 0.04 ?(a) Is X a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS)ANSWER:(b) What must be the probability of choosing a unit with 10 rooms? P(X = 10) =(c) What is the probability that a unit chosen at random has more than 5 rooms? P(X > 5) =(d) What is the probability that a unit chosen at random has three rooms? P(X=3) =(e) What is the probability that a unit chosen at random has between four and six rooms? P(4 \leq X \leq 6)
Mathematics
1 answer:
vichka [17]3 years ago
5 0

Answer:

a) DISCRETE

b) P(X=10)=0.04

c) P(X>5)=0.64

d) P(X=3)=0.1

e) P(4≤X≤6)=0.74

Step-by-step explanation:

X       3      4       5      6       7      8     9      10

P(X) 0.1 0.24 0.33 0.17 0.05 0.05 0.04  0.00

(NOTE: the probability for X=10 is not shown)

a) X is a discrete random variable, as is possible value are only integer numbers (number of rooms: 3, 4, 5, ... , 10).

b) The probability of choosing a unit with ten rooms is: P(X=10)=0.04, according to the table.

c) The probability of choosing a unit that has more than 5 rooms is equal to the sum of probablities of choosing a unit with 6, 7, 8, 9 or 10 rooms.

P(X > 5) = P(6)+P(7)+P(8)+P(9)+P(10)

P(X > 5) = 0.17+0.05+0.05+0.04+0.00 = 0.31

d) The probability that a unit chosen at random has three rooms is P(X=3)=0.1.

e) The probability that a unit chosen at random has between four and six rooms is

P(4≤X≤6)=P(4)+P(5)+P(6) = 0.24+0.33+0.17 = 0.74

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Answer:

Part A)

  • The observation from the the table indicates that if the value of variable x increases, the value of variable y also increases.

Part B)

  • y=6x+10 is the function that bets fits the data.

Part C)

  • The slope defines that a single worker is able to produces 6 units.Thus, for a given number of workers x, the units produced would be 6x.
  • The y-intercept defines that for the total number of units produced y by x number of workers, 10 units would be added.

Step-by-step explanation:

Part A)

We know that

  • Negative correlation means when one variable decreases, then the other variable also decreases.
  • Positive correlation means when one variable increases, then the other variable also increases.

Given the table data

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The observation from the the table indicates that if the value of variable x increases, the value of variable y also increases.

Thus, the two variables i.e. Number of employees (x) and Number of Products (y)  will have positive correlation.

Please check the attached graph in figure a to determine that the positive correlation as the value of variable x increases when the value of variable y also increases.

Part B)

Given the table data

Number of employees (x)

      (x)     0       25       50      75       100     125     150      175      200

Number of Products (y)

     (y)      10     160     310     460     610     760     910     1060     1210

As we know that the point slope form

y=mx+b

where m is the slope and b is the y-intercept.

Lets take the point (0, 10) and point (200, 1210)

As

m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}

m=\frac{1210-10}{200-0}

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As

y-y_{1} = m(x-x_{1})

m = \frac{y-y_{1}}{x-x_{1}}

Taking any point, let say (25, 160), and putting in

m = \frac{y-y_{1}}{x-x_{1}}

6\:=\:\frac{y-160}{x-25}

y=6x+10

Hence, y=6x+10 is the function that bets fits the data.

Part C)

As we have determined the equation

y=6x+10

Here,

  • Slope = m = 6
  • y-intercept = 10

The slope defines that a single worker is able to produces 6 units.Thus, for a given number of workers x, the units produced would be 6x.

The y-intercept defines that for the total number of units produced y by x number of workers, 10 units would be added.

Keywords: slope, function, linear function, correlation

Learn more about correlation from brainly.com/question/14688591

#learnwithBrainly

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