Answer to Practice Problem 1
The average commute time for workers in a large metropolitan area is 35 minutes with a standard deviation of 8 minutes. A researcher takes a random sample of 64 workers.
- What is the probability that the sample mean commute time is less than 33.5 minutes?
- The mean and standard deviation are:
- $\mu_{\bar{x}}$ = $\mu$ = 35
- $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{8}{\sqrt{64}} = \frac{8}{8} = 1.0$
- The probability is found by finding the area of the left tail of the sampling distribution using a Z-Table or a calculator
- On a Z-Table,
- The z-score is $z = \frac{33.5 - 35}{1.0} = \frac{-1.5}{1.0} = -1.5$
- Look at the area left of z = -1.5
- On a TI-83/84, DISTR –> 2:normalcdf(
- 2:normalcdf(-9999,33.5,35,1) if using the values from the problem
- 2:normalcdf(-9999,-1.5,0,1) if using the z-score (gives the same answer)
- Probability = 0.067 = 6.7%
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