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. What

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): You can put this solution on YOUR website!

mu = 89 = population mean
sigma = 3 = population standard deviation

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.

Answer: About 84.134%

RELATED QUESTIONS
in a certain population, the mean score on a test is 105. If the distribution of scores... (answered by stanbon)

Scores on a test have a mean of 73 and Q3 is 83. The scores have a distribution that is... (answered by Theo)

Suppose the scores for a certain test follow a normal distribution with a mean of 78 and... (answered by Fombitz)

George needs to earn a B in his Algebra class. His current test scores are 88,81,78, and... (answered by swincher4391)

susan needs to earn a B in her algebra class. her current test scores are 79, 81, 77 and... (answered by Fombitz)

Scores on a test have a mean of 73 and 10 percent of the scores are above 87. The scores... (answered by oscargut)

The distribution of certain test scores is a nonstandard normal distribution with a mean... (answered by stanbon)

The average mark on a test in an algebra class is 80. If the two lowest scores of 34 and... (answered by richwmiller)

Mike needs to earn a C and his intermediate algebra class. his current test scores are 65 (answered by Fombitz)