We used a simulation performed on the ATLANTA COMMUTING TIMES. We have a populat

Question

We used a simulation performed on the ATLANTA COMMUTING TIMES. We have a population mean of 29.11 minutes and a standard deviation of 20.71831.

If you took a sample of 30 commuters from this population, what is the probability that the average commuting time from your sample will be at least 35 minutes?

What is the probability that your sample mean from a sample of 60 commuters will be at least 35 minutes?

Why does the sample size make these two probabilities different? (how does sample size effect probabilities?)

Explanation / Answer

Ans:

Given that

population mean=29.11

standard deviation=20.72

when sample size=30

standard error of mean=20.72/sqrt(30)=3.78

z=(35-29.11)/3.78=1.56

P(z>=1.56)=0.0594

when sample size=60

standard error of mean=20.72/sqrt(60)=2.67

z=(35-29.11)/2.67=2.21

P(z>=2.21)=0.0136

As,when sample size increases,standard error of mean decreases and z value will increase,so probability of sample mean being atleast 35 will decrease.

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