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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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3 years ago
Después de 15 meses de haber prestado un capital al 5% de rédito, tengo que pagar de interés Q468.75. ¿Qué capital se ha prestad
Aleonysh [2.5K]

The capital borrowed, or the principal when the interest was Q468.75 is <u>Q7500</u>.

The principal P, amount borrowed, at a certain rate of interest R%, for  a time of T years, giving an interest of I, can be calculated using the formula:

P = (I * 100)/(R * T).

In the question, we are asked to find the capital borrowed, that is, the principal, when the user pays Q468.75 after 15 months at 5% of income.

Thus, Interest (I) = Q468.75, rate of interest (R) = 5%, and time (T) = 15 months = 15/12 years = 1.25 years.

Thus, the principal P, can be calculated by substituting the values in the formula: P = (I * 100)/(R * T).

P = (468.75*100)/(5*1.25),

or, P = 46875/6.25,

or, P = 7500.

Thus, the capital borrowed, or the principal when the interest was Q468.75 is <u>Q7500</u>.

The provided question is in Spanish. The question in English is:

"After 15 months of having borrowed capital at 5% of income, I have to pay Q468.75 in interest. What capital has been borrowed?"

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2 years ago
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