Question

consider a normal population with u= 75 and o= 10. a sample of at least which size needs to be obtained in order to achieve a standard error or om= 2.00 or less.

Answer 1

Answer: Choice C)

n = 25

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Step-by-step explanation:

The standard error formula for the mean is

`\sigma_(M) = (\sigma)/(√(n))\\\\`

Since we want this 2.00 or less, this means,

`\sigma_(M) \le 2.00\\\\(10)/(√(n)) \le 2.00\\\\10 \le 2.00√(n)\\\\2.00√(n) \ge 10\\\\√(n) \ge (10)/(2.00)\\\\√(n) \ge 5\\\\n \ge 5^2\\\\n \ge 25\\\\`

The sample size needs to be n = 25 or larger.

In other words, the sample size needs to be at least 25.