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The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.(a) What proportion of the students scored at least 26 points on this test, rounded to five decimal places? (b)What is the 31 percentile of the distribution of test scores, rounded to three decimal places?

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Using z-scores the answers are found to be, part(a) 0.02280 and part(b) = 22.980 points

What is z-score?

Z-score is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.

What is the formula for z-score?

The formula for z-score is,

z = (x - µ) / a

where µ is the mean of data set and a is the standard deviation of the data

For part (a),

z = 26-22/2

z = 2.00

P(x>26) = 0.5 - 0.4772

P(x>26) = 0.02280

For part(b),

To find the value of x we first need to find the value of z-score. z-score at 100 - 31 - 50 = 19% = 0.19

At an area of approximately 0.19, the z-score is 0.49

Using above formula, 0.49 = (x -22)/2

x = 22.980

To learn more about formula of z-score visit given below link:

https://brainly.com/question/29470513

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