Question 1202308: Good Afternoon, for my other question please help me with this question since I'm finding it difficult to solve it myself.
Normal Distribution
The distribution of SAT scores in math for an incoming class in statistical analysis has a
mean of 750 and a standard deviation of 25. Assume that the scores are normally distributed.
(a) Find the probability that an individual’s SAT score is less than 700.
(b) Find the probability that an individual’s SAT score is between 730 and 780.
(c) Find the probability that an individual’s SAT score is greater than 760.
(d) What scores will the top 4% of students have?
(e) Find the standardized values for students scoring 510, 590, 640, and 820 on the test.
Explain what these mean.
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Good Afternoon, for my other question please help me with this question
since I'm finding it difficult to solve it myself.
Normal Distribution
The distribution of SAT scores in math for an incoming class in statistical analysis has a
mean of 750 and a standard deviation of 25. Assume that the scores are normally distributed.
(a) Find the probability that an individual’s SAT score is less than 700.
(b) Find the probability that an individual’s SAT score is between 730 and 780.
(c) Find the probability that an individual’s SAT score is greater than 760.
(d) What scores will the top 4% of students have?
(e) Find the standardized values for students scoring 510, 590, 640, and 820 on the test.
Explain what these mean.
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A normal distribution curve is a bell shaped curve.
(a) In part (a), the probability is the area under this specific normal curve
on the left from the raw mark value of 700.
You may use a regular calculator TI-83 or TI-84 with the standard function
normalcdf (stands for normal cumulative distribution function). You write
z1 z2 mean SD <<<---=== formatting pattern
P = normalcdf(-9999, 700, 750, 25)
Alternatively, you may go to website https://onlinestatbook.com/2/calculators/normal_dist.html
and use free of charge online calculator there.
This online calculator has simple and perfect interface. Any beginner student can start use it
from the day zero, and after 5 minutes working with it, this student will understand the subject
in all details. This online calculator is a perfect teacher.
The answer which you will get is the number (the probability) of 0.0228 (rounded).
(b) In part (b), the probability is the area under this specific normal curve
between the raw mark values from 730 to 780.
You may use a regular calculator TI-83 or TI-84 with the standard function
normalcdf (stands for normal cumulative distribution function). You write
z1 z2 mean SD <<<---=== formatting pattern
P = normalcdf(730, 780, 750, 25)
Alternatively, you may go to website https://onlinestatbook.com/2/calculators/normal_dist.html
and use free of charge online calculator there.
The answer which you will get is the number (the probability) of 0.6731 (rounded).
(c) In part (c), the probability is the area under this specific normal curve
on the right of the raw mark values 760.
You may use a regular calculator TI-83 or TI-84 with the standard function
normalcdf (stands for normal cumulative distribution function). You write
z1 z2 mean SD <<<---=== formatting pattern
P = normalcdf(760, 9999, 750, 25)
Alternatively, you may go to website https://onlinestatbook.com/2/calculators/normal_dist.html
and use free of charge online calculator there.
The answer which you will get is the number (the probability) of 0.3446 (rounded).
So, I answered your questions (a), (b) and (c) and explained on how
you can solve similar problems using a regular hand calculator or online calculator.
For other questions, (d) and (e), it requires a SEPARATE post.
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