The year 2021 marked the end of a drought experienced by Australia since 2017. Some of the consequences of the drought was a sharp increase in hay prices, and the scarcity of hay. This impacted thousands of farmers and livestock owners across the country. In 2019, the price of teff hay increased to $32.00 for one bale. Bales of teff have an average weight of 21kgs, which is assumed to be normally distributed, with a standard deviation of 1kg. Using the above information, answer the following questions, and make sure to explain your answers by commenting on the choice and appropriateness of the test/methodology used in your calculations:

1. Find the probability that if a horse owner buys one bale of teff hay, that bale will weight more than 21.5kgs. (10 points)

2. Find the probability that if a horse owner buys 6 bales of teff hay, the mean weight of the 6 bales is more than 21.5kgs. (10 points)

3. If a random sample of 25 bales had an average weight of 20.3kgs, what would you conclude about the validity of the claim that the average weight of a bale of teff hay is 21kgs? (10 points)