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24 February, 19:55

Analysis showed that the mean arrival rate for vehicles at a certain Shell station on Friday afternoon last year was 4.5 vehicles per minute. How large a sample would be needed to estimate this year's mean arrival rate with 98 percent confidence and an error of ± 0.5?

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  1. 24 February, 21:38
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    25

    Step-by-step explanation:

    use a Poisson process to model the arrival.

    the mean rate of arrivals is λ=4.5

    The standard deviation is calculated as:

    σ==√λ = 2.1213

    The z-value for a 98% CI is z=2.3262.

    If the 98% CI has to be within a error of 0.5 then:

    Ul-Ll=2z*σ/√n=2*0.5=1

    √n=z*σ=2.3262*2.1213=4.9346

    √n=4.9346 and n = 4.9346^2=24.35 rounded to 25

    The sample size needed is n=25.
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