Question

A standardized test has a mean of 50 and a standard deviation of 4. Find the probability of test scores in the following ranges.
1. between 42 and 58
2. below 46
3. between 46 and 54

Answer 1

Have you learned about the standard normal distribution? Because I know of two ways to work this kind of problem but I've only ever bothered to learn one ...

Answer 2

i honestly dont know....aha i dont even know what standard deviation is

Answer 3

To tell you the truth, I don't really either, just the calculation for it ... But I can tell you that it has something to do with how likely a given data point will *deviate* from the mean. Have you learned anything about random variables, namely the following transformation:
\[Z=\frac{Y-\mu}{\sigma},\]
where \(Z\) is standard, normally distributed random variable,
\(Y\) is a normally distributed random variable,
\(\mu\) is the mean of \(Y\), and
\(\sigma\) is the standard deviation of \(Y\)?

Answer 4

If any of this doesn't ring any bells, I think you're expected to figure the problem out with the method I don't know...

Answer 5

thank you for your help!