Dinner at Home. Choose a parent with children under age 18 in the United States

Question

Dinner at Home. 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 XX for short. Based on a large sample survey, here is a probability model for the answer you will get NightsProbability00.061020.0730.0840.1150.1760.1570.36Nights01234567Probability0.0600.070.080.110.170.150.36 (a) Is this a valid finite probability model? Yes No (b) What is P(X<4)P(X<4)? P(x<4)P(x<4) = (c) Express the event "eat dinner together at home at least once a week" in terms of XX. {X2}{X2} {X1}{X1} {X1}{X1} {X2}{X2} {X>1}{X>1} What is the probability of this event?

Explanation / Answer

following infromation has been generated using the given data. if there is any discripency please share

(a) Is this a valid finite probability model? Yes

since sum of the total probability is 1, so this is fininte probability model

(b)P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=0.06+0+0.07+0.08=0.21

(c)Express the event "eat dinner together at home at least once a week"

P({X1} )=1-P(X<1)=1-P(X=0)=1-0.06=0.94

Nights Probability 0 0.06 1 0.00 2 0.07 3 0.08 4 0.11 5 0.17 6 0.15 7 0.36 total 1

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