On an exam with a mean of μ = 70, you have a score of X = 75; What st. dev. would the highest position...
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On an exam with a mean of μ = 70, you have a score of X = 75; What st. dev. would the highest position...

[From: ] [author: ] [Date: 11-06-22] [Hit: ]
1.2.3.4.Help I dont understand the Q or the answer........
On an exam with a mean of μ = 70, you have a score of X = 75. Which of the following values for the standard deviation would give you the highest position within the class?

1. σ = 5
2. σ = 10
3. cannot determine from the information given
4. σ = 1

Help I don't understand the Q or the answer...

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(x - μ) / σ = z

the highest z score will give you the answer

(75 - 70) / 5 = z
1 = z

(75 - 70) / 10 = z
.5 = z

(75 - 70) / 1 = z
5 = z

if σ = 1, your score would be really hard to beat

only .000000287 of the class would be expected to to better than you

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the answer is σ = 1 because
conceptually,
x=μ+- σ

so if your class has σ of 1 then the average variation in class is plus/minus 1 is 69 to 71

hence if your score is 75 which is greater than 71, that means your will have highest chance of securing highest position within the class.

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4 becasue average +- 3(1) encompases 99.7% of population. So on the high side it would be 70 + 3 = 73. Your score of 75 relative to 73 would put above the 99.7% level.
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