Pre-Algebra Due now Please help, thank you
2 answers:
Answer:
1. The is between 3 and 4.
2. The is between 7 and 8.
3. The is between 4 and 5.
4. The is between 9 and 10.
5. The is between 6 and 7.
Step-by-step explanation:
1. : 10 is near the perfect squares 9 and 16, which would mean its answer is between their square roots which are 3 and 4.
2. : 10 is near the perfect squares 49 and 64, which would mean its answer is between their square roots which are 7 and 8.
3. : 10 is near the perfect squares 16 and 25, which would mean its answer is between their square roots which are 4 and 5.
4. : 10 is near the perfect squares 81 and 100, which would mean its answer is between their square roots which are 9 and 10.
5. : 10 is near the perfect squares 36 and 49, which would mean its answer is between their square roots which are 6 and 7.
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Answer:
a)
b)
c) The value of height that separates the bottom 75% of data from the top 25% is 9.9745.
Step-by-step explanation:
1) 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".
2) Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
3) Part b
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
4) Part c
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 0.75 of the area on the left and 0.25 of the area on the right it's z=0.6745. On this case P(Z<0.6745)=0.75 and P(z>0.6745)=0.25
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 75% of data from the top 25% is 9.9745.
To calculate the square root, you can either use the √symbol on a calculator or you can manually find it using Prime Factorization. For non-perfect squares, Prime Factorization is the way to go.
The first two steps work for solving large perfect squares as well.
1. Divide your number into perfect square factors.
2. Take the square roots of your perfect square factors.
3. If your number doesn't factor perfectly, reduce your answer to simplest terms.
4. If needed, estimate. In some cases if you have memorized some of the square roots, you can estimate where the number would be.
ie.
you know that 
and 
, so you can estimate that the would be between 7 and 8 but closer to 8.
5. <span>Alternatively, reduce your number to its lowest common factors as your first step.</span><span> Finding perfect square factors isn't necessary if you can easily determine a number's prime factors (factors that are also prime numbers).
ie. </span>
=
=
=
Hope this helped!!!
The first two steps work for solving large perfect squares as well.
1. Divide your number into perfect square factors.
2. Take the square roots of your perfect square factors.
3. If your number doesn't factor perfectly, reduce your answer to simplest terms.
4. If needed, estimate. In some cases if you have memorized some of the square roots, you can estimate where the number would be.
ie.
5. <span>Alternatively, reduce your number to its lowest common factors as your first step.</span><span> Finding perfect square factors isn't necessary if you can easily determine a number's prime factors (factors that are also prime numbers).
ie. </span>
=
=
=
Hope this helped!!!