Expand the expression and combine like terms: 1+4(6p-9)
2 answers:
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Answer:
And if we solve for a we got
So the value of height that separates the bottom 90% of data from the top 10% is 4.624.
So then the best answer for this case would be:
C. 4.64
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 the weights 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 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
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 90% of data from the top 10% is 4.624.
So then the best answer for this case would be:
C. 4.64
Answer:
A) The applicant's SAT z-score has to be positive and large.
Step-by-step explanation:
The zscore measures how much above or below the mean a value is in a normally distributed sample. The value can be a grade, for example.
In a set with mean and standard deviation
, the zscore of a measure X is given by
.
When the zscore of X is negative and large, this means that the grade is on the very low side(very below the mean).
When the zscore of X is negative and small, this means that the grade is on the low side(a bit below the mean).
When the zscore of X is close to 0, the grade is close to the mean.
When the zscore of X is positive and small, this means that the grade is on the high side(a bit above the mean).
When the zscore of X is positive and large(Z > 1), this means that the test score is on a very high side.
The problem states that:
To get admitted to top universities, the applicant's SAT (Scholastic Aptitude Test) score must be on a very high side. So, the correct answer is:
A) The applicant's SAT z-score has to be positive and large.