Z-Score for a Discrete Random Variable
The table below defines the probability distribution for the random variable X, the number of miles of highway laid by a construction crew in one day.
| Weather Condition | Miles of Highway Laid (X) | Probability P(X) |
|---|---|---|
| Clear | 5 | 0.6 |
| Rain | 2 | 0.3 |
| Snow | 1 | 0.1 |
Based on this distribution, would an outcome of 10 miles of highway laid in a single day be considered surprising? Justify your conclusion in terms of the number of standard deviations this value is from the mean.
A
No; 10 miles is exactly equal to the mean plus one standard deviation.
B
Yes; 10 miles is about 1.5 standard deviations above the mean.
C
No; 10 miles is within 1 standard deviation of the mean.
D
Yes; 10 miles is approximately 3.9 standard deviations above the mean.
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