Choose a parent with children under age 18 in the United States at random and as
ID: 3133364 • Letter: C
Question
Choose a parent with children under age 18 in the United States at random and ask, “How many nights a week out of seven does your family eat dinner together at home?” Call the response X for short. Based on a large sample survey, here is a probability model for the answer you will get:6
(a)Verify that this is a valid finite probability model.
(b)Describe the event X < 4 in words. What is P(X < 4)?
(c)Express the event “eat dinner together at home at least once a week” in terms of X. What is the probability of this event?
Explanation / Answer
(a)To be a valid probability Model,sum of all the probabilities should be equal to 1
Hence sum(probabilities)=0.05+0.07+0.08+0.1+0.17+0.15+0.38=1
Hence Yes this is a valid Probability Model
b)X<4, means the number of nights the family eats dinner together is less than 4 or which is less than or equal to 3
Hence P(X<4)=P(0)+P(1)+P(2)+P(3)=0.05+0+0.07+0.08=0.2
c)Event:Eat dinner together at home at least once a week=X>=1
P(X>=1)=P(X>0)=1-P(X=0)=1-0.05=0.95