During a certain week the mean price of gasoline in the New

During a certain week the mean price of gasoline in the New England region was $2.714 per gallon. A random sample of 32 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.695 and $2.725 that week? Assume sigma=$0.045

Solution

During a certain week the mean price of gasoline in the New England region was $2.714 per gallon. A random sample of 32 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.695 and $2.725 that week? Assume sigma=$0.045

Standard error = 0.045 /sqrt(32) =0.007955

Z value for 2.695,   z= (2.695-2.714)/0.007955 = -2.388   = -2.39( 2 decimals)

Z value for 2.725,   z= (2.725-2.714)/0.007955 = 1.3828 = 1.38( 2 decimals)

P( 2.695<x<2.725) = p( -2.39 < z<1.38)

= p( z < 1.38)