Caroline's favorite animal is the dolphin. One of the dolphins in the tank is 4 meters long. What is its length in centimeters?
2 answers:
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Answer:
And if we solve for a we got;
So the value of height that separates the bottom 95% of data from the top 5% is 11.64
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent certain lifetime of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got;
So the value of height that separates the bottom 95% of data from the top 5% is 11.64
It says that there was an error with my answer, but I don't know what, so I screenshotted what I typed and attached them as 4 images below:
X miles per hour - <span> speed of the boat in still water
(x - 2) - speed up the river
(x + 2) - speed down the river
</span>
= 
30 * (x + 2) = 38 * (x - 2)
30x + 60 = 38x - 76
- 8x = - 136
x = 17 miles per hour - <span>the speed of the boat in still water.</span>
(x - 2) - speed up the river
(x + 2) - speed down the river
</span>
30 * (x + 2) = 38 * (x - 2)
30x + 60 = 38x - 76
- 8x = - 136
x = 17 miles per hour - <span>the speed of the boat in still water.</span>