Suppose you are in search of the perfect chocolate chip cookie recipe. You've made a lot of batches of chocolate chip cockies and have been taking careful notes on what ingredient amounts result in the most delicious cookies. Based on your experience, you're pretty sure: the optimal average flour weight is μ=0.280 kg. To test your hypothesis, you make 10 batches of cookies using your optimized recipe and note the exact amount of flour you put in each batch. Suppose further that the amount of flour in a batch of cookies is known to be normally distributed with σ=0.09 kg. Your cookles all turn out well, so you decide that if the average amount of flour you used in your 10 -batch sample (X) is more than 0.05 kg different from 0.280, you will reject your null hypothesis that μ=0.280 and rewrite the recipe. Using a test procedure with a test statistic of X and a rejection region consisting of values of X≥0.33, calculate the probability of a type 1 error (a).