SOLUTION: Mr. Jackson is looking at test scores for his Algebra 2 class. The scores on the Unit 2 Test follow a normal distribution, with a mean of 89 and a standard deviation of 3.
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-> SOLUTION: Mr. Jackson is looking at test scores for his Algebra 2 class. The scores on the Unit 2 Test follow a normal distribution, with a mean of 89 and a standard deviation of 3.
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Question 1194773: Mr. Jackson is looking at test scores for his Algebra 2 class. The scores on the Unit 2 Test follow a normal distribution, with a mean of 89 and a standard deviation of 3.
What percent of learners scored 86 or better? Show all work and provide the answer. Answer by math_tutor2020(3817) (Show Source):
For the raw score x = 86, it converts to the following z score
z = (x - mu)/sigma
z = (86 - 89)/3
z = (-3)/3
z = -1
This raw score is exactly one standard deviation below the mean.
Now use a table like this one here https://www.ztable.net/
Highlight the row that starts with -1 at the very left
Highlight the column that has 0 at the top
This row and column intersect at the value 0.15866
This tells the reader
P(Z < -1) = 0.15866 approximately
So,
P(Z > -1) = 1 - P(Z > -1)
P(Z > -1) = 1 - 0.15866
P(Z > -1) = 0.84134
which is also approximate
This means
P(x > 86) = 0.84134 approximately
If you wanted, you can use a calculator to get better precision.
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