A large sized coffee at Starbucks is called a venti, which meanstwenty in Italian because a venti cup is supposed to hold 20 ouncesof coffee. Jonathan doesn’t believe that his venti always has anaverage of 20 ounces of coffee in it, so he wants to testStarbucks’ claim. He randomly chooses 50 Starbucks locations andgets a cup of venti coffee from each one. He then measures theamount of coffee in each cup and finds 30 of them had less than 20ounces of coffee. This seems suspicious to Jonathan, who figuredStarbucks would have tried to keep about a 50-50 split betweenunder-filled and overfilled coffees if they are going to honor the“venti” claim. a. Calculate a 95% confidence interval for the trueproportion of venti coffees from Starbucks that have less than 20ounces in them. b. (6 points) Is Starbucks’ claim that a venti cuphas 20 ounces of coffee reasonable based on the confidence intervalyou calculated in (a)? Why? Please answer in 1-2 sentences. c. (6points) Suppose that the true population proportion of Starbucksventi coffees with less than 20 oz is .50. What is the probabilitythat someone like Jonathan would have gotten a result as extreme asthe result he found in the study above? d. (6 points) Undeterred,Jonathan continues his quest to uncover the venti scandal andeventually builds a sample of venti cups of coffee from 500randomly selected Starbucks locations. Of these, 300 had less than20 ounces of coffee. Based on this sample, calculate a 95%confidence interval for the true proportion of venti coffees fromStarbucks that have less than 20 ounces in them. e. (6 points) IsStarbucks’ claim that a venti cup has 20 ounces of coffeereasonable based on the confidence interval you calculated in (d)?Why? Please answer in 1-2 sentences.