In 2020, and given the ongoing scarcity of teff hay, a horse owner decided to buy enough bales to last them a year. They thus bought 210 bales. They calculated that the average weight of the bales they bought is 21.2kgs, with a standard deviation of 0.5kg. Using the information provided by the sample of 210 bales, 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: 4. Find a 95% confidence interval estimate of the average weight of a bale of teff hay.(10 points) 5. If the horse owner wanted to estimate the mean weight of a bale of teff hay within 0.7kgs, with a confidence level of 90%, how many bales of teff hay should they have bought? (15 points) 6. From their observations within their sample, can the horse owner conclude that the mean weight of a bale of teff hay is greater than 21kgs? (15 points) 7. What would the answer to question 6. be if the horse owner used the population standard deviation of 1kg observed in 2019 rather than the sample standard deviation? (15 points) It is known that 30% of teff hay bales contain high sugar levels, i.e more than 10% of ESC+Starch. 8. What is the probability that in the sample of 210 bales bought by the horse owner, more than 33% have high sugar content? (15 points)