What is the correlation coefficient r for the data set? enter your answer to the nearest hundredth in the box. r = x y 25 240 26
1 answer:
The use of the excel tool given in the image above will give you the correlation coefficient of r for the data set is as r=-0.96
<h3>What is the correlation coefficient about?</h3>Note that one have to find first, the mean of all of your the x-values, and then one can find the mean of all of the y-values.
Note that one can use the excel to find the mean which will be 28.4 and 214.6 for both.
The next step is to find the standard deviation for x and y. Then, you have to put it into the formula that is given for the correlation coefficient."
When you use the excel, R will be -0.9647 and when you round up to the nearest hundredth, the answer will be -0.96.
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Answer:
a. 99.30% of the woman meet the height requirement
b. If all women are eligible except the shortest 1% and the tallest 2%, then height should be between 58.32 and 68.83
Explanation:
<em>According to the survey</em>, women's heights are normally distributed with mean 63.9 and standard deviation 2.4
a)
A branch of the military requires women's heights to be between 58 in and 80 in. We need to find the probabilities that heights fall between 58 in and 80 in in this distribution. We need to find z-scores of the values 58 in and 80 in. Z-score shows how many standard deviations far are the values from the mean. Therefore they subtracted from the mean and divided by the standard deviation:
z-score of 58 in= = -2.458
z-score of 80 in= = 6.708
In normal distribution 99.3% of the values have higher z-score than -2.458
0% of the values have higher z-score than 6.708. Therefore 99.3% of the woman meet the height requirement.
b)
To find the height requirement so that all women are eligible except the shortest 1% and the tallest 2%, we need to find the boundary z-score of the
shortest 1% and the tallest 2%. Thus, upper bound for z-score has to be 2.054 and lower bound is -2.326
Corresponding heights (H) can be found using the formula
and
Thus lower bound for height is 58.32 and
Upper bound for height is 68.83