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). Say X is the number of passengers out of the 20 that are part of the frequent rider club. a. Was type of distribution does X follow? Write the probability mass function (f (x)), and name b. What is the expected number of passengers that are part of the frequent rider club. Interpret c. Say each passenger is charged $3.00 for their tickets. What is the expected revenue? What is its parameters this value for the shuttle operator (in a sentence or two). the variance of the revenue? d. Now say each passenger in the frequent rider club are charged $2.00 for their tickets and the regular passengers (not in the frequent rider club) are charged S4.50 for their tickets. What is the expected revenue?

Question

Autumn Lowe

Mathematics

10 February, 23:40

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). Say X is the number of passengers out of the 20 that are part of the frequent rider club. a. Was type of distribution does X follow? Write the probability mass function (f (x)), and name b. What is the expected number of passengers that are part of the frequent rider club. Interpret c. Say each passenger is charged $3.00 for their tickets. What is the expected revenue? What is its parameters this value for the shuttle operator (in a sentence or two). the variance of the revenue? d. Now say each passenger in the frequent rider club are charged $2.00 for their tickets and the regular passengers (not in the frequent rider club) are charged S4.50 for their tickets. What is the expected revenue?

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Answers (1)

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Edgar Villanueva · Answer 1

a. Discrete probability distribution, frequent rider club, 0.65 of 20

b. 13

c. $60

d. $57.50

Step-by-step explanation:

a. X follows a discrete probability distribution because it involves discrete random variables which have probability mass function and frequency.

f (x) = 0.65 of 20 passengers

b. if 0.65 0f 20 passengers are frequent riders,

then, the frequent riders will be 13 passengers

c. expected revenue will be $3 * 20 passengers which will be $60.

the total number of passengers given tickets is 20 and the price for each is $3. thus, making the parameters to be price and number of passengers.

d. if the frequent riders are charged $2, then the amount paid by this group will be $2*13 which is $26

and if $4.50 is paid by the regular passengers it will be $4.50 * (20-13) which is $31.50.

therefore, expected revenue will be $26+$31.50 equals $57.50