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 commute time of a single passenger is less than 33.5 minutes?
- The probability is found by finding the area of the left tail of a standardized normal distribution using a Z-Table or a calculator
- On a Z-Table,
- The z-score is $z = \frac{33.5 - 35}{8} = \frac{-1.5}{8} = -0.1875
- Look at the area left of z = -0.1875
- On a TI-83/84, DISTR –> 2:normalcdf(
- 2:normalcdf(-9999,33.5,35,8) if using the values from the problem
- 2:normalcdf(-9999,-0.3125,0,1) if using the z-score (gives the same answer)
- Probability = 0.425 = 42.5%
Click here to return to the lecture notes.