Yes (B) should be the right answer.
What any point (x, y) at the 95 percentile line denotes ?
In the month x, out of 50 years approx 47 - 48 year's rainfall is below y mm.
What any point (x, y) at the 5 percentile line denotes ?
In the month x, out of 50 years approx 2 - 3 years's rainfall is below y mm.
Logically 5 percentile curve must always lie below 95 percentile which actually is the case here.
(I) ON AVERAGE, it rains more in July than in December : It is a direct conclusion from the "Average" curve on the graph.
Since July lies above in Average curve than December, it implies that on average, July is more rainy than December.
So it must be true.
(II) EVERY YEAR, the amount of rainfall in August is more than that in January : The plot gives no information about the rainfall during individual years, it is a combined plot of 50 years.
Out of 50 years, there are 2 -3 years when the rainfall may drop to a very minimal value (say 0 mm) in August & in the same year it is also possible that 100 mm Rain falls in January.
So the given information is insufficient to deduce this fact.
Hence false.
Above two deductions are strong enough to answer this question, as only option B is consistent with the conclusions derived so far.
(III) July rainfall can be estimated with better confidence than February rainfall : It can be observed that the difference between 95 percentile plot and 5 percentile plot at July is smaller than that at February (thin shaped graph at July & thick at February).
It shows that for 90% of the data, variance in rainfall at February is higher than variance in rainfall at July.
It means that in July most of the times(90%) the rainfalls are densely spread around average rainfall, but in Feb they are sparsely spread around the average rainfall.
Densely spread means less chances of committing errors during estimation.
So it should also be true.
(IV) In August there is AT LEAST 500 mm of rainfall : This is false, as the plot does not provides any information about the minimum & maximum rainfall in any Month.There might be no rainfall (0 mm) during August in a particular year.
