Respuesta :
Answer:
(a) P(x < 2) = 0.871
(b) P(x ≥ 1) = 0.320
(c) P(1 ≤ x ≤ 3) = 0.299
Step-by-step explanation:
We are given the probability distribution of the number of dogs per household in a small town .
Dogs | Households
0 | 0.680
1 | 0.191
2 | 0.079
3 | 0.029
4 | 0.0130
5 | 0.008
(a) Find the probability of randomly selecting a household that has fewer than two dogs.
Fewer than two dogs mean having 0 dog or 1 dog so
P(x < 2) = P(x = 0) + P(x = 1)
P(x < 2) = 0.680 + 0.191
P(x < 2) = 0.871
(b) Find the probability of randomly selecting a household that has at least one dog.
at least one dog means one or greater than one so
P(x ≥ 1) = P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)
P(x ≥ 1) = 0.191 + 0.079 + 0.029 + 0.0130 + 0.008
P(x ≥ 1) = 0.320
Alternatively:
P(x ≥ 1) = 1 - P(x < 1)
P(x ≥ 1) = 1 - P(x = 0)
P(x ≥ 1) = 1 - 0.680
P(x ≥ 1) = 0.320
(c) Find the probability of randomly selecting a household that has between one and three dogs, inclusive.
P(1 ≤ x ≤ 3) = P(x = 1) + P(x = 2) + P(x = 3)
P(1 ≤ x ≤ 3) = 0.191 + 0.079 + 0.029
P(1 ≤ x ≤ 3) = 0.299
