Chobani yogurt is made using a special straining technique to remove excess liquid. This process yields a thicker, creamier yogurt with more protein per serving than a regular yogurt.32 Suppose the...

Chobani yogurt is made using a special straining technique to remove excess liquid. This process yields a thicker, creamier yogurt with more protein per serving than a regular yogurt.32 Suppose the amount of protein in a six-ounce cup of Chobani yogurt is normal with mean 15.5 grams and standard deviation 0.8 gram. A six-ounce cup of Chobani yogurt is selected at random from the assembly line.

a. What is the probability that there are more than 16.5 grams of protein in the cup of yogurt?

b. If the amount of protein in a cup of yogurt is between 14 and 17 grams, the manufacturing process is consider to be in control. What is the probability that the process is considered in control? Out of control?

c. Suppose the cup of yogurt has less than 16 grams of protein. What is the probability that it has more than 15 grams?

 d. Suppose that six cups of yogurt are selected at random. What is the probability that at least three cups have at least 16.5 grams of protein?