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One Mean $z$-interval: Finding the Minimum Sample Size

APSTAT-OCEZ8K

You are sampling from a population with a known standard deviation of $10$ and an unknown population mean. You want to construct a $99\%$ confidence interval, with a margin of error of no more than $4$.

What is the minimum sample that will produce this interval?

A

$6$

B

$7$

C

$25$

D

$41$

E

$42$