Determine distribution to use

[BlahBlee]

I am given sample size, mean and standard deviation and I have to determine which distribution to use.

For example: A random sample of 40 college students has a mean earnings of $3120 with a standard deviation of $677 over the summer months. Determine whether a normal distribution, a t-distribution or neither should be used.

The rule I was taught was to use t-distribution when the sample size is under 30 and otherwise use z-distribution. I applied this rule to the sample sizes given, marking sample sizes less than 30 as t-distribution but that came back wrong. I don't understand when to use a normal distribution as I have no rule for that.

 

[Harry_the_cat]

If you do not know the population standard deviation, you need to use the t-distribution.

If you do know the population standard deviation, you need to use the z-distribution.

Do you know the population standard deviation?

 

[Romsek]

the z-distribution is the normal distribution

Additionally to what HarryTC said you use the t distribution with a small sample size \(\displaystyle n < 30\)