1) The amount of Mangoes that are produced each year by a farmer in Waka Village is normally distributed. The standard deviation of the bags of mangoes is identified as 0.04 grams. Mangoes that too small and unripe are not bagged. Using your knowledge of hypothesis testing and a 95% confidence level, execute a two - tailed to prove the claim that = 0.50 grams. The sample mean is 0.51 grams and the sample size is 25 bags of mangoes.

2) Jacksonville Traders manufactures battery operated toy cars that would last 20,000 hours. Random samples of 14 battery operated toy cars were examined. The standard deviation of the sample was 1750 hours. What is the probability that the toy cards, when examined in a test, will not last more than 19800 hours?

3) Suppose there are three different types of cakes that are sold at Lina's Bakery. There are 4 cheesecakes, 5 vanilla sponge cakes and 2 black forest cakes. Tom takes at random 2 of these cakes without replacement. What is the probability that he takes 2 different types of cakes upon his selection?

4) Suppose the Fiji Rugby Sevens team is in the grand final of HK Sevens championship. Experts have assigned a probability of 60% that Fiji will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lost championship, they win the first game 25% of the time. The first game is over against NZ and Fiji has lost. Present the above information in a tree diagram and calculate the probability of Fiji winning the championship given that they have lost their first game.