A task force is studying the need for an additional bicycle path on a large univ

Question

A task force is studying the need for an additional bicycle path on a large university campus. It is assumed that the distribution of bicyclists using a path between classes is normally distributed with a population variance of about 64. A random sample of 7 existing bicycle paths showed that the sample mean number of bicyclists using a path between classes was 33.

A group of interested students took its own sample of 5 different bicycle paths, and computed a confidence interval for the population mean that ranged from (16.0 , 25.173 ). What is the probability content (or the level of confidence) of this interval?

Explanation / Answer

here as we know that mrgin of error =z*Std deviation/sqrt(n)=(upper confidence limit-lower confidence limit)/2

z*sqrt(64/5)=(25.173-16)/2

z=1.28

for above z is crtiical value for 80% confidene interval

hence probability content of this interval is 0.8 or 80%.

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