Question

Help with probability please?

1) A small train at an amusement park is carrying passengers. Half of the passengers are 6 years old, 1/10 are 7 years old, 1/5 are 8 years old and 1/5 are 9 years old. What is the expected age for one of the passengers on the train?
A) 6 years
B)7.1 years
C)8 years
D) 8.5 years

2)Which probability distribution table corresponds with this frequency table?

X 1 2 3 4 5
F 3 7 2 3 5

A) X 1 2 3 4 5
P 0.3 0.7 0.2 0.3 0.5

B) X 1 2 3 4 5
P 0.2 0.2 0.2 0.2 0.2

C X 1 2 3 4 5
P 0.15 0.35 0.1 0.15 0.25

D) X 1 2 3 4 5
P 1.5 3.5 1 1.5 2.5

Answer 1

1.)

Number of passengers who are 6 years old
`=(1)/(2)`

Number of passengers who are 7 years old
`=(1)/(10)`

Number of passengers who are 8 years old
`=(1)/(5)`

Number of passengers who are 9 years old
`=(1)/(5)`

E(X=6+X=7+X=8+X=9)

=6 × P(6) +7 ×P(7)+8×P(8)+9×P(9)

`=6* (1)/(2)+7* (1)/(10)+8* (1)/(5)+9* (1)/(10)\\\\ =3+0.7+1.6+0.9\\\\ =3+2.3+0.9\\\\=6.2`

Option A :6 (approx) ,appears true.

2.)

Sum of total frequency =3+7+2+3+5=20

`P(1)=(3)/(20)=0.15, P(2)=(7)/(20)=0.35,P(3)=(2)/(20)=0.10, P(4)=(3)/(20)=0.15,P(6)=(5)/(20)=0.25`

Option C: X 1 2 3 4 5

P 0.15 0.35 0.10 0.15 0.25

is true.