Finding sample size given info on confidence interval

[eterna]

Homework Statement

Suppose that an investigator believes that virtually all values in the population are between 38 and 70. The appropriate sample size for estimating the true population mean within 2 units with 95% confidence level is approximately how much?

Homework Equations

Variance of the sampling distribution of size n = Variance of the population distribution / n

The Attempt at a Solution

I think I'm solving
1.96(SD of the sampling distribution of size n)=2

But I don't think there's any information given on the population variance so I don't know what to do.

 

[Joffan]

Worst case, half the population values are 38 and half are 70. What's the variance in that case?

 

[pasmith]

Homework Statement

Suppose that an investigator believes that virtually all values in the population are between 38 and 70. The appropriate sample size for estimating the true population mean within 2 units with 95% confidence level is approximately how much?

Homework Equations

Variance of the sampling distribution of size n = Variance of the population distribution / n

The Attempt at a Solution

I think I'm solving
1.96(SD of the sampling distribution of size n)=2

But I don't think there's any information given on the population variance so I don't know what to do.

Use the three standard deviation rule.

 

[eterna]

Use the three standard deviation rule.

so is the sd = (70-38)/6 ?