The table below indicates the accuracy of a local weather report with respect to

Question

The table below indicates the accuracy of a local weather report with respect to rain or no rain over the past year. This table gives the results of 365 consecutive days and compares whether it rained or not to whether or not rain was predicted.

If one day is randomly selected from these 365 days, what is the probability of the following? (Round your answers to 3 significant digits*.)

*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.

0.123      0.0123      0.0120      0.00123      0.102      0.350      0.300

(a) the prediction was correct
P(the prediction was correct) =

(b) it rained given that it was predicted to rain
P(it rained | rain was predicted) =

(c) it did not rain when it was predicted to not rain
P(no rain | no rain was predicted) =

(d) Based on these results, is this weather forecast better at predicting rain or better at predicting no rain?

The weather forecast is better at predicting rain or is The weather forecast is better at predicting no rain.

     Did it actually rain?      Yes           No Report Predicted Rain     109           12 Report Predicted No Rain     40            204

Explanation / Answer

from above:

a)  P(the prediction was correct) =(109+204)/365 =0.858

b) P(it rained | rain was predicted) = 109/121=0.901

c)

P(no rain | no rain was predicted) = 204/244 =0.836

d)

as we can see that probability in part b is greater therefore weather forecast is better at predicting rain

rain? yes No total report predicted rain 109 12 121 report predicted no rain 40 204 244 total 149 216 365

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.