35. Chebychey's Theorem Old Faithful is a famous geyser at Yellowstone National Park. From a sample with 32. the mean duration o
f Old Faithful's eruptions is 3.32 minutes and the standard deviation is 1.09 minutes. Using Chebycher's Theorem, determine at least how many of the eruptions lasted between 1.14 minutes and 5.5 minutes. (Source: Yellowstone National D 36. Chebycher's Theorem The - 577
1 answer:
Answer:
The probability that the eruptions lasted between 1.14 min and 5.5 minutes is greater than 75%
Step-by-step explanation:
The explanation can be found in the attached picture. Chebyshev's <u>inequality </u>was used. It predicts the probability of the random variable to be in ( mean- K* standard dev< x < mean + K*standard dev).
Note: K must be greater than 1
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so the syrup is just water and sugar, we know that the sugar percent is just 12%, and that happens to be 5grams.
now 100% - 12% is 88%, so the 88% leftover will just be water.
if 12% is 5g, how much is 88%?
Answer:
If we solve for k we can do this:
So then we have at last 75% of the data withitn two deviations from the mean so the limits are:
Step-by-step explanation:
We don't know the distribution for the scores. But we know the following properties:
For this case we can use the Chebysev theorem who states that "At least of the values lies between
and
"
And we need the boundaries on which we expect at least 75% of the scores. If we use the Chebysev rule we have this:
If we solve for k we can do this:
So then we have at last 75% of the data withitn two deviations from the mean so the limits are: