Question 1150701


{{{Z-score = (7.5 - 6)/3= 1.5/3 = 0.5}}} 


Look up {{{0.5}}} on a z-table.  The result is {{{0.6915}}}.  This means there is a {{{0.6915}}} probability the random variable will be below {{{7.5}}}.


{{{Z-score = (5.7 - 6)/3 = (-0.3)/3 = -0.1}}}


Look up {{{-0.1}}} on a z-table.  The result is {{{0.4602}}}.  The means there is a {{{0.4602}}} probability the random variable will be below {{{5.7}}}.


The find the probability the random variable will be between {{{7.5}}} and {{{5.7}}}, simply {{{subtract}}} the two probabilities we found (above) from one another:


{{{0.6915 - 0.4602 = 0.2313}}}


So, there is a {{{0.2313}}} probability the random variable will fall between {{{7.5 }}}and {{{5.7}}}.