Answer:
[tex]E=3.4363[/tex]
Step-by-step explanation:
#Given a significance level of [tex]\alpha=1-CI=1-0.90=0.1[/tex] and
[tex]\bar x=36, \ \sigma=12.1 \ n=41,[/tex] the critical value is,[tex]z_\alpha_/_2=z_\alpha_/_0_._0_5=1.645[/tex]
#the margin of error can then be calculated as:
[tex]E=z_\alpha_/_2\times\frac{\sigma}{\sqrt n}=1.645\times \frac{12.1}{\sqrt 33}\\\approx 3.4363[/tex]
Hence the margin of error is 3.4363
