How to get the probability from the mean of a random variable?

In summary, a professor is trying to determine the probability that a student's test score will exceed 75 on a final examination, which is known to have a mean of 65. The student has attempted to find the standard deviation and variance, but is stuck and seeking help. It is assumed that the test scores are normally distributed.
  • #1
EGD Eric
2
0

Homework Statement


From past experience, a professor knows that the test score of students taking a final examination is a random variable with mean 65.

Give an upper bound on the probability that a student's test score will exceed 75.


Homework Equations



None that I know of.

The Attempt at a Solution


I tried seeing if I could get the standard deviation, in the hopes that I could do something with that, but I don't know how to even get the variance.

I've tried looking at this problem from a bunch of different angles, writing it out, etc.. I'm seriously stuck! Any help or hints would be greatly appreciated!
 
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  • #2
Is this normally distributed?
 
  • #3
I think so.
 

Related to How to get the probability from the mean of a random variable?

1. What is a random variable?

A random variable is a numerical value that is determined by the outcome of a random process. It can take on different values with certain probabilities associated with each value.

2. How is the mean of a random variable calculated?

The mean of a random variable is calculated by multiplying each possible value by its corresponding probability and then summing all of these values together. This is also known as the expected value.

3. Can the mean of a random variable be used to determine the probability?

No, the mean of a random variable cannot directly determine the probability. The mean only gives an overall measure of central tendency for the values of a random variable, but it does not provide information about the individual probabilities of each value.

4. Is there a formula for calculating the probability from the mean of a random variable?

No, there is no single formula for calculating the probability from the mean of a random variable. The probability is dependent on the specific distribution of the random variable.

5. How can the probability from the mean of a random variable be approximated?

The probability from the mean of a random variable can be approximated by using the central limit theorem. This theorem states that as the sample size increases, the distribution of sample means will approach a normal distribution, allowing for the estimation of probabilities from the mean.

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