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?

239

Step-by-step explanation:

Given : Confidence level : 99%

Significance level :

Margin of error : E = 3 minutes

Population standard deviation :

To find : Numbers of observations are required. (Minimum Sample size)

Formula :

Using z-value table,

Two-tailed z-value for :

Using given values , we get

Hence, the minimum number of observation is required = 239

both equations and proportions are better.