City planners estimate that they can attract 20% of commuters who currently use

Question

City planners estimate that they can attract 20% of commuters who currently use bus service to a new light rail to the downtown area. Suppose that 71000 independent commuters use bus service daily. Approximate the probability that more than 10500 commuters will use the light rail daily Round your answer to three decimal places (e.g. 98.765). (b) Approximate the number of daily commuters who will use the light rail which will be exceeded with probability only 0.05 Round your answer to the nearest integer (e-g. 9876) The number of daily commuters who will use the light rail which will be exceeded with probability only 0.05 is

Explanation / Answer

(a)Given that

Total no of independent commuters who use bus daily =Total no of sample (A)=71000

Number of commuters who will use the light rail daily (B)=10500 (more than this)

so

Probablity of commuters who use the light rail daily P(B)=B/A=10500/71000 =0.1478 (more than this)

(b)Given that

Total no of independent commuters use bus daily =Total no of sample (A)=71000

   Let Number of commuters who will use the light rail daily =B

according to question P(B)=0.05

now we know that P(A)=B/A

Hence B=A*P(A)=71000*0.05 =3550

so

The number of cummuters who will use the light rail which will be exceeded with probablity 0.05=3550

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