A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ a. becomes wider. b. becomes narrower. c. becomes 100.1 to 120.1. d. does not change.

Using confidence interval concepts, the correct option is:

b. becomes narrower

The margin of error of a confidence interval is given by:

In which:

The lower the confidence level, the lower the value of z, hence, the margin of error decreases and the interval becomes narrower, which means that option b is correct.

A similar problem is given at link

b. becomes narrower.

Step-by-step explanation:

Since the 95% confidence interval for a population mean could find out from 100 to 120

And based on this, the coefficient confidence level is declined to 0.90

Therefore the confidence interval for mean should become narrowed

As a 95% confidence interval represents narrower and 99% confidence interval represents wider

Therefore the option B is correct

the answer will be the last one