Question

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 ? = $0.045.

Answer 1

Solution :

Given that,

mean = = $2.714

standard deviation = = $0.045

n =32

= 2.714

= / n = 0.045/ 32=0.0080

P($2.695< <$2.725 ) = P[(2.695 - 2.714) / 0.0080< ( - ) / < (2.725 - 2.714) /0.0080 )]

= P( -2.38< Z <1.38 )

= P(Z < 1.38) - P(Z <-2.38 )

Using z table,  

=   0.9162 -0.0087

= 0.9075