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Basics of Z-Score and Normal Model
68-95-99.7 rule
Inverse Norm Q's
Z-Score Q's
Miscellaneous
100
What is a standard of measurement that tells us how many standard deviations that the value is away from the mean
z-score
100
What % of all values lie within 1 standard deviation on either side of the mean
68%
100
Find z so that 10% of the values lie to the left of z
-1.28155
100
The average people in a calculus class in a college is 34 kids with a standard deviation of 2. What is the z-score of there being a class with 39 kids
2.5
100
What percentage of all values lie within 2 standard deviation above or below the mean
95%
200
What function in your calculator do you use to find the probability of getting a value given a z-score
Normalcdf
200
What % of all values lie within 3 standard deviation on either side of the mean
99.7%
200
Find z so that 58% of curve lies within -z and z
0.806421 (100-58=42%, 42%/2=21% and 100-21% = 79%, then do invnorm(0.79,0,0)
200
The average test score in the class was a 88, with a standard deviation of 5 points. Jake received a 80. What is the z-score of his test grade.
-1.6
200
What is the equation to find the z score
(your value - mean)/standard deviation
300
What shape should the graph of a normal model be?
Bell-shaped
300
If you are given a sample in which the model is normal and 95% of the values are included, how many standard deviations away from the mean should we expect the most extreme values within the 95% be
2 standard deviations from either side of the mean
300
The mean grade on the test was 82 with a standard deviation of 6. If the model is normal what is the assumed cutoff grade that the top 5% of students in the class received for a grade
91.8691
300
A kid got his test back, but there was no score on the test. He was given that his grade had a z-score of 0.8. He was also given that the mean grade in his class was a 87 with a standard deviation of 5. What grade did he receive on his test
91
300
If your value is below the mean, is your z-score going to be positive or negative
negative
400
What two things do you need to find the z-score of a given value
Mean and standard deviation
400
Without using a calculator, given that the model is normal, what percentage of values should lie over 1 standard deviation above the mean
16% ( 100-68=32, 32/2=16%) you divide by 2 since we are only looking at values over 1 standard deviation, and not including below 1 standard deviation.
400
The average test score in a class was a 85 with a standard deviation of 7. Ryan received a 75. The teacher said that the bottom 10% of the class would have to retake the test. Assuming that the model is normal, does Ryan have to retake the test?
yes
400
A kid finds out that his test grade of 94 had a z-score of 2.25. If the mean test grade in his class was a 85, what was the standard deviation of the grades in his class.
4
400
To find the z-score given a percentile, what function on your calculator should you use
Inverse normal
500
If the graph of a model is bimodal and skewed, is the model normal
No
500
What is the probability that a kid gets a test grade that is 3 standard deviations below the mean, given that the model is normal
0.15% (100-99.7= 0.3%, 0.3/2=0.15%) we divide by 2 since we are only looking at values below 3 standard deviations, and we are not including above 3 standard deviations
500
Find z so that 30% of the curve lies between 0 and z
0.841621 (if 30% is between 0 and z, and that is half the curve so 50% is to the left of 0 so 30+50 = 80% so you do invnorm(0.8,0,1)
500
Mike finds that his test grade of 82 had a z-score of -1.5 and that the standard deviation of the grades in his class was 6. What was the mean test grade in his class
91
500
What two things should the graph of a model be to determine that it is normal
should be unimodal and roughly symmetric