Four buses carrying 148 students from the same school arrive at a football stadium. the buses carry, respectively, 40, 33, 25, and 50 students. one of the students is randomly selected. let x denote the number of students that were on the bus carrying the randomly selected student. one of the 4 bus drivers is also randomly selected. let y denote the number of students on her bus. (a) which of e[x] or e[y] do you think is larger? why? (b) compute e[x] and e[y].

E[X] is larger than  E[Y]

E[X]  = 39.283784  and E[Y] = 37

Step-by-step explanation:

Given data

total students = 148

bus 1 students = 40

bus 2 students = 33

bus 3 students = 25

bus 4 students = 50

to find out

E[X] and E[Y]

solution

we know bus have total 148 students and 4 bus

so E[X] is larger than  E[Y] because maximum no of students are likely to chosen to bus and probability of bus is 1/4  as chosen students

and probability  of 40 i.e. P(40)  students = 40/148

P(33) = 33/148

P(25) = 25 / 148

P(50) = 50 / 148

first we find out i.e

E[X]  = 40 P(40) + 33 P(33)+  25 P(25)+  50 P(50)

E[X]  = 40  (40/148) + 33 (33/148)+  25 (25/148)+  50 (50/148)

E[X]  = 39.283784

and

y is bus chosen

E[Y] = 1/4 (40+ 33 + 25 + 50)

so E[Y] = 1/4 (40+ 33 + 25 + 50)

E[Y] = 1/4 (148)

E[Y] = 37

so E[X]  = 39.283784  and E[Y] = 37

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: