Question 1200360
(i) The z-score of {{{250}}} is {{{(250-215)/10=3.5}}}. We can use a z-table to see that the proportion of cups that don't overflow is {{{0.99977}}}, so the proportion of cups that do overflow is {{{1-0.99977=0.00023}}}, or {{{0.023%}}}
(ii) The z-score of {{{200}}} is {{{(200-215)/10=-1.5}}}. We can again use a z-table to get {{{0.06681}}}, which is the probability the cup contains less than 200 ml. So the probability that a cup contains at least 200 ml is {{{1-0.06681=0.93319}}}.
(iii) We need to find the value on a z-table that is closest to 0.98, since the z-table gives us the area to the left of the curve. We see that {{{2.05}}} is the closest, and a {{{2.05}}} z-score translates to size cups of {{{215+10*1.05=highlight(225.5)}}} ml.