the table below shows the ages of houses to the nearest year in a neighborhood. using the age of the houses…

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, $p_x(x)$, of a randomly chosen house?\n| age of house | number of houses |\n| ---- | ---- |\n| 1 | 15 |\n| 2 | 20 |\n| 3 | 25 |\n| 4 | 30 |\nprobability distribution
Answer
Explanation:
Step1: Calculate total number of houses
$15 + 20+25 + 30=90$
Step2: Calculate probabilities for each age
For age $1$: $P(X = 1)=\frac{15}{90}=\frac{1}{6}\approx0.167$ For age $2$: $P(X = 2)=\frac{20}{90}=\frac{2}{9}\approx0.222$ For age $3$: $P(X = 3)=\frac{25}{90}=\frac{5}{18}\approx0.278$ For age $4$: $P(X = 4)=\frac{30}{90}=\frac{1}{3}\approx0.333$
The given graph shows probabilities approximately as $0.15$ for $x = 1$, $0.2$ for $x = 2$, $0.25$ for $x = 3$ and $0.3$ for $x = 4$ which is consistent with our calculated values.
Answer:
The given graph shows the probability - distribution of a randomly - chosen house.