2. The summer monsoon rains bring 80% of a country\'s rainfall and are essential
ID: 3053466 • Letter: 2
Question
2. The summer monsoon rains bring 80% of a country's rainfall and are essential for the country's agriculture. Records going back more than a century show that the amount of monsoon rainfall varies from year to year according to a distribution that is approximately Normal with mean 858 millimeters (mm) and standard deviation 88 mm. Use the 68-95-99.7 rule to answer the following questions.
(a) Between what values do the monsoon rains fall in 95% of all years?
From _______mm to __________mm
Explanation / Answer
2)
the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively
Thus, for 95% +- 2 std deviations from mean
Thus, from 858- 2*88 mm to 858+ 2*88 mm
i.e. 682 mm to 1034 mm
3)
Z= (x-u)/ ?
Thus, Z = (34-24.8)/6.9
Z = 1.33
P(X>34) = P(Z>1.33)
= 1- 0.9082
= 0.0918
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