A shuttle operator has sold 20 tickets to ride the shuttle. All passengers (ticket holder) are independent of each other, and the probability that a passenger is part of the frequent rider club is 0.65 (65% chance they are part of the group and 35% chance they are not). Let X be the number of passengers out of the 20 that are part of the frequent rider club. a. What type of distribution does X follow? Write the probability mass function (f(x)), and name its parameters. b. What is the expected number of passengers that are part of the frequent rider club. Interpret this value for the shuttle operator (in a sentence or two). c. What is the probability that exactly 10 ticket holders are part of the frequent rider club? Write out the theoretical form and use R to compute a numerical value.
3. A shuttle operator has sold 20 tickets to ride the shuttle. All passengers (ticket holder) are independent of each other, and the probability that a passenger is part of the frequent rider club is 0.65 (65% chance they are part of the group and 35% chance they are not). Let X be the number of passengers out of the 20 that are part of the frequent rider club.
a. What type of distribution does X follow? Write the probability mass
b. What is the expected number of passengers that are part of the frequent rider club. Interpret this value for the shuttle operator (in a sentence or two).
c. What is the probability that exactly 10 ticket holders are part of the frequent rider club? Write out the theoretical form and use R to compute a numerical value.
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