A restaurant manager tracks the number of people in every party to sit at a specific table every day for a week, and then compiles the results into a probability distribution as shown in the table: Number of People , X 1 23 4 5 6 Relative Frequency, P(X) 0.050.460.18 0.22 0.06 0.03 a.) There is a 25% chance that a party will contain 5 or more people. b.) There is a 50% chance that a party will contain 4 or more people. c.) There is a 50% chance that a party will contain 2 or fewer people. d.) There is a 75% chance that a party will contain 3 or more people.
a.) The probability of a party having 5 or more people is the sum of the probabilities for X = 5 and X = 6:
P(X ≥ 5) = P(X = 5) + P(X = 6) = 0.22 + 0.06 = 0.28
This is greater than 25%, so the statement is false.
b.) The probability of a party having 4 or more people is the sum of the probabilities for X = 4, X = 5, and X = 6:
P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = 0.18 + 0.22 + 0.06 = 0.46
This is greater than 50%, so the statement is true.
c.) The probability of a party having 2 or fewer people is the sum of the probabilities for X = 1 and X = 2:
P(X ≤ 2) = P(X = 1) + P(X = 2) = 0.05 + 0.46 = 0.51
This is greater than 50%, so the statement is true.
d.) The probability of a party having 3 or more people is the sum of the probabilities for X = 3, X = 4, X = 5, and X = 6:
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0 + 0.18 + 0.22 + 0.06 = 0.46
This is not greater than 75%, so the statement is false.