7 Fence panels come in two sizes, large and small. The lengths of the large panels are normally distributed with mean 198 cm and standard deviation 5 cm . The lengths of the small panels are normally distributed with mean 74 cm and standard deviation 3 cm .
- Find the probability that the total length of a random sample of 3 large panels is greater than the total length of a random sample of 8 small panels.
One large panel and one small panel are selected at random.
- Find the probability that the length of the large panel is more than \(\frac { 8 } { 3 }\) times the length of the small panel.
Rosa needs 1000 cm of fencing. The large panels cost \(\pounds 80\) each and the small panels cost \(\pounds 30\) each. Rosa's plan is to buy 5 large panels and measure the total length. If the total length is less than 1000 cm she will then buy one small panel as well.
- Calculate whether or not the expected cost of Rosa's plan is cheaper than simply buying 14 small panels.