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Z-Score and Proportion

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Toby's trucking company determined that the distance traveled per truck per year is normally distrinuted, with a mean of 50.0 thousand miles and a standard deviation of 12.0 thousand miles.

a. What proportion of trucks can be expected to travel between 34.0 and 50.0 thousand miles in the year?
b. What percentage of trucks can be expected to travel between 30.0 or above 60.0 thousand miles in the year?
c. How many miles will be traveled by at least 80% of the trucks?
d. What are your answers to (a) through (c) if the standard deviation is 10.0 thousand miles?

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Solution Summary

The solution provides step by step method for the calculation of z-score and proportions. Formula for the calculation and interpretations of the results have also been included.

Solution provided by:
Anwesha Ghosh, MSc
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  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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