Question: 1. Consider the following probability distribution function of the random variable X, which represents the number of people in a group (party) at a

1. Consider the following probability distribution function of the random variable X,

1. Consider the following probability distribution function of the random variable X, which represents the number of people in a group (party) at a restaurant. P(x) 1 0.05 2 0.35 3 0.15 4 5 0.10 6 0.05 7 0.05 Total 0.05 a. Fill in the missing value for P(4) in the table. b. Find the population mean , the mean number of people in a group (party) at the restaurant. HINT: Recall that u (x P(x)). C. Find the probability that the next party will have more than 4 people. Include the probability statement, using probability notation. P(X > 4) = d. Find the probability that the next party will have at least 2 people, but no more than 5 people. Include the probability statement, using probability notation. Use Insert>Equation command from the pulldown menu. e. Find the probability that the next party will have at most 3 people. Include the probability statement, using probability notation. Use Insert>Equation command from the pulldown menu.

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