It is 170 miles from Bruce’s house to the city where his brother lives. On his last trip to visit his brother, he drove for 2 ho
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
Answer:
36 miles
Step-by-step explanation:
(Imagine a huge triangle on a perfectly open space-- not with streets or houses or cornfields.)
The dimensions of the two sides given are multiples of a classic Pythagorean Triple: 3, 4, 5.
9 is 3x3, 12 is 3x4 so the remaining side would be 3x5 15
Add those 3 sides to get the total distance, 36 miles.