c, the answer is going by 3, so it is c.
The easiest way to do this is to write the decimals with equal amount of places after the dot and you'll see it more clearly:
1.09 = 1.090
1.901 = 1.901
1.9 = 1.900
1.19 = 1.190
So from the least to the greatest:
1.090
1.190
1.900
1.901
In a form you gave at the beginning:
1.09 < 1.19 < 1.9 < 1.901
Answers:
The z scores are approximately:
- Care of Magical Creatures: z = 0.333
- Defense Against the Dark Arts: z = 0.583
- Transfiguration: z = -0.263
- Potions: z = -0.533
From those scores, we can say:
- Best grade = Defense Against the Dark Arts
- Worst grade = Potions
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Further Explanation:
We'll need to convert each given score to a corresponding standardized z score.
The formula to use is
z = (x - mu)/sigma
where,
- x = given grade for each class
- mu = mean
- sigma = standard deviation
Let's find the z score for the Care of Magical Creatures class
z = (x - mu)/sigma
z = (3.80 - 3.75)/(0.15)
z = 0.333 approximately
Repeat this process for the Defense Against the Dark Arts score.
z = (x - mu)/sigma
z = (3.60 - 3.25)/(0.60)
z = 0.583 approximately
And for the Transfiguration class as well
z = (x - mu)/sigma
z = (3.10 - 3.20)/(0.38)
z = -0.263 approximately
The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.
Now do the final class (Potions) to get this z score
z = (x - mu)/sigma
z = (2.50 - 2.90)/(0.75)
z = -0.533 approximately
This grade is below average as well.
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To summarize, we have these z scores
- Care of Magical Creatures: z = 0.333
- Defense Against the Dark Arts: z = 0.583
- Transfiguration: z = -0.263
- Potions: z = -0.533
Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.
I’m pretty sure the answer is either D or E but I’m not positive !
The absolute value of -8 is 8 and the absolute value of 5 is 5. Absolute value is basically the number's distance from 0 on a number line, basically how many numbers it is away from 0. For that reason, it's always positive, regardless of whether or not the number is positive or negative. Hope this helped!
