A cow ate 38 pounds of grass, the cow now weighs 394 pounds. How much would the cow weigh if it did not eat the grass?
2 answers:
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We have a sequence that meets the given criteria, and with that information, we want to get the sum of all the terms in the sequence.
We will see that the sum tends to infinity.
So we have 5 terms;
A, B, C, D, E.
We know that the sum of each term and its neighboring terms is 15 or 25.
then:
- A + B + C = 15 or 25
- B + C + D = 15 or 25
- C + D + E = 15 or 25
Now, we want to find the sum of all the terms in the sequence (not only the 5 given).
Then let's assume we write the sum of infinite terms as:
Now we group that sum in pairs of 3 consecutive terms, so we get:
So we will have a sum of infinite of these, and each one of these is equal to 15 or 25 (both positive numbers). So when we sum that infinite times (even if we always have the smaller number, 15) the sum will tend to be infinite.
Then we have:
If you want to learn more, you can read:
Answer:
The mean of the distribution is about 53.9 and standard deviation is about 16.5 marks.
Step-by-step explanation:
Use the trick of transforming the given random variable one that is standard normal distributed, aka a z-score, then look up the two percentile values in z-score tables to get two equations with two unknowns.
So, let x be the variable describing the marks of a student, and
the standardized equivalent of that (mu - mean, sigma - standard deviation).
We are looking for values of mu and sigma. At this point we'd be out of luck, but, wait, we're given two bits of info: the 10% point (aka, 90th percentile) and the 20% point (can be interpreted as 100-20th percentile). For each point we can use z-score tables to look up the corresponding values of z (just search for z tables). I found:
z-score for the 10% point: z_10=1.28
z-score for the 20% point: z_20=-0.84
That gives us two equations:
and can be solved for mu and sigma (do the work on your end, I am showing my result):
The mean of the distribution is about 53.9 and standard deviation is about 16.5 marks.