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?

Question

Mathematics

Kaylah Bishop

11 November, 14:18

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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Answers (1)

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Kieran Chandler · Answer 1

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.