Question

The scores on a standardized test are normally distributed. If a random sample of standardized test scores is taken and the confidence interval is (92.3,120.7), what is the sample mean x¯?

Answer 1

Answer: 106.5

Explanation:

We know that, Confidence interval for population mean is given by :-

( Sample mean - Margin of error , Sample mean + Margin of error)

Given: confidence interval is (92.3, 120.7).

i.e. Sample mean - Margin of error = 92.3 (i)

Sample mean + Margin of error = 120.7 (ii)

Adding (i) and (ii) , we get

2( Sample mean ) = 213

⇒ Sample mean = 106.5

Hence, the sample mean
`(\overline{x})` = 106.5