The table below shows the ages of houses to the nearest year in a neighborhood. using the age of the houses as the random variable, x, which graph shows the probability distribution, px(x), of a randomly chosen house?

age of house
number of houses
1
15
2
20
3
25
4
30
a probability distribution is shown. the probability of 1 is 0.16; 2 is 0.22; 3 is 0.28; 4 is 0.33.
a probability distribution is shown. the probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.4.
a probability distribution is shown. the probability of 1 is 0.65; 2 is 0.1; 3 is 0.12; 4 is 0.13.
a probability distribution is shown. the probability of 1 is 0.15; 2 is 0.2; 3 is 0.25; 4 is 0.3.

The probability distribution of X is given by,

P(X = x)     0.17    when x = 1

                0.22   when x = 2

               0.28    when x = 3

               0.33    when x = 4

             = 0   otherwise

Step-by-step explanation:

According to the question, X is the random variable denoting age of a house to the nearest year in  a neighborhood.

From the given data we can construct the following table -

Age of house(X)          Frequency     Relative frequency

                                                            (Almost equal to)

1                                       15                     0.17

2                                      20                    0.22

3                                      25                    0.28

4                                      30                    0.33

So, the probability distribution of X is given by,

P(X = x)     0.17    when x = 1

                0.22   when x = 2

               0.28    when x = 3

               0.33    when x = 4

             = 0   otherwise

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt