elizabethhart9
Answered

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?

A6 years

B)7.1 years

C)8 years

D8.5 years

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


X 1 2 3 4 5

F 3 7 2 3 5

AX 1 2 3 4 5

P 0.3 0.7 0.2 0.3 0.5

BX 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

DX 1 2 3 4 5

P 1.5 3.5 1 1.5 2.5

Verified Answer :

Answer:

1.)

Number of passengers who are 6 years old \(=\frac{1}{2}\)

Number of passengers who are 7 years old \(=\frac{1}{10}\)

Number of passengers who are 8 years old \(=\frac{1}{5}\)

Number of passengers who are 9 years old \(=\frac{1}{5}\)

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

  =6 × P(6) +7 ×P(7)+8×P(8)+9×P(9)

  \(=6\times \frac{1}{2}+7\times \frac{1}{10}+8\times \frac{1}{5}+9\times \frac{1}{10}\\\\ =3+0.7+1.6+0.9\\\\ =3+2.3+0.9\\\\=6.2\)

Option A :6 (approx) ,appears true.

2.)

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

\(P(1)=\frac{3}{20}=0.15, P(2)=\frac{7}{20}=0.35,P(3)=\frac{2}{20}=0.10, P(4)=\frac{3}{20}=0.15,P(6)=\frac{5}{20}=0.25\)

Option C:  X 1 2 3 4 5

P 0.15 0.35 0.10 0.15 0.25

is true.

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