How do I do this and what is the answer ?
1 answer:
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Answer:
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 grades of a population, and for this case we know the distribution for X is given by:
For this case we have two conditions given:
or equivalently
And the best way to solve this problem is using the normal standard distribution and the z score given by:
So we can find a value from the normal standard distribution that accumulates 0.1 and 0.9 of the area in the left, for this case the two values are:
We can verify that P(Z<-1.28) =0.1[/tex] and P(Z<1.28) =0.9[/tex]
And then using the z score we have the following formulas:
(1)
(2)
If we add equations (1) and (2) we got:
We can multiply both sides of the equation by and we got:
And then we can find the standard deviation for example from equation (1) and we got:
So then the answer would be:
Answer:
Correlation coefficient ≈ 0.9445
This indicates that the weight of a student increases as the height of the student increases.
Step-by-step explanation:
The rest of the question is the following table
value of x (<u>height</u>) are 58, 59, 60, 62, 63, 64, 66, 68, 70
Value of y (<u>weight</u>) are: 122, 128, 126, 133, 145, 136, 144, 150, 151
=======================================================
To calculate the correlation coefficient we will use the following form:
So, n (the number of terms) = 9
∑x = 570, ∑y= 1236, ∑ x²= 36234, ∑ y²= 170694 and ∑xy=78617
So, the correlation coefficient =
∴ r = 0.9445
So, weight of a student increases as the height of the student increases.