The following question from a Statistics test does not make sense to me.
Question:
Data from the past 100 years show that rainfall during April varies randomly from day to day. Over that period the mean amount in the month has been 60 cm, with no noticeable upward or downward trend. By 20th April this year, 30 cm of rain had fallen. The total amount expected in the month is thus: A. 30cm B. 40cm C. 50cm D. 60cm
Answer:
C - 50cm
My understanding
If the mean rainfall in April is 60cm and this has been pretty stable over the past 100 years, then the mean rainfall expected would be 60cm for this year.
Now, my only interpretation is that they want to check that I know means do not entail that each year had 60cm of rainfall. Some years were lower, others were higher, but they averaged out to 60cm. As the question says "no noticeable upward or downward trend", would I just assume that though this is a lower than average month, it should be around 50cm overall and not too far below 60cm?
Is that all it's asking?
The mean amount of rainfall during one day of April is (1/30)(60cm) = 2cm. There are 10 days left in April, so the expected amount of rainfall for those days is 20cm, and therefore the total expected rainfall for the month is 30cm + 20cm = 50cm.