How Do Standard Deviations Affect Probability in Statistics Problems?

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Homework Statement

My mean is 5.80
My standard deviation is 0.64
The largest number does not exceed 7

1) What is the probability the probability of randomly selecting a number, and the number being over 2 σ from the mean.

2) For a sample of 30, what is the probability the mean will be over 2 SD from the mean? 2. The attempt at a solution

1) It must be 0%, correct? As 2 sd greater than the mean exceeds all values there are?

2) This is the one that puzzles me. I genuinely do not understand why 30 samples do not have to be taken. Perhaps, it also has something to do with 2 σ from the mean exceeding all values?

 

[Ray Vickson]

Homework Statement

My mean is 5.80
My standard deviation is 0.64
The largest number does not exceed 7

1) What is the probability the probability of randomly selecting a number, and the number being over 2 σ from the mean.

2) For a sample of 30, what is the probability the mean will be over 2 SD from the mean? 2. The attempt at a solution

1) It must be 0%, correct? As 2 sd greater than the mean exceeds all values there are?

2) This is the one that puzzles me. I genuinely do not understand why 30 samples do not have to be taken. Perhaps, it also has something to do with 2 σ from the mean exceeding all values?

You are correct about question 1). While a laywer could argue that the question 2) is ambiguous, I would think the meaning is clear enough: the σ in question 2) refers to the standard deviation of the sample mean, not the standard deviation of the underlying random variable. In other words, you need a σ that is different from 0.64; do you know what the correct value should be?

RGV