4) We want a 99% confidence interval for the average amount of time (in minutes) spent commuting to work in a large city. The interval is to have a margin of error of no more than 3 minutes, and the amount of time spent commuting has a normal distribution with a standard deviation  = 18 minutes. What numbers of observations are required?

Accepted Solution

Answer: 239Step-by-step explanation:Given : Confidence level : 99%Significance level : [tex]\alpha=1-0.99=0.01[/tex]Margin of error : E = 3 minutesPopulation standard deviation : [tex]\sigma=18[/tex]To find : Numbers of observations are required. (Minimum Sample size)Formula : [tex]n=(\dfrac{z_{\alpha/2}\cdot\sigma}{E})^2[/tex]Using z-value table, Two-tailed z-value for [tex]\alpah=0.01[/tex] : [tex]z_{\alpha/2}=2.576[/tex]Using given values , we get [tex]n=(\dfrac{2.576\cdot18}{3})^2\\\\=(15.456)^2\\\\=238.887936\spprox239[/tex]Hence, the minimum number of observation is required = 239