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Assume the commuting times of American workers follow a normal distribution with mean mu=23 minutes and...

Assume the commuting times of American workers follow a normal distribution with mean mu=23 minutes and standard deviation sigma=5 minutes. A random sample of 16 American workers is taken. What is the probability that the sample mean commuting time is greater than 25 minutes?

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Answer #1

The commuting times of American workers follow a normal distribution with mean = 23 minutes, and standard deviation of 5 minutes.

A random sample of 16 American workers is taken.

We have to find the probability that the sample mean is greater than 25 minutes.

If X be the random variable denoting the sample mean of these 16 workers, then X follows normal distribution with mean 23 and standard deviation of 5/sqrt(16), ie. 1.25.

We have to find

Where, phi is the distribution function of the standard normal variate.

From the standard normal table this becomes

So, the probability that the sample mean commuting time is greater than 25 minutes, is 0.0548.

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