Question

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. Suppose the amount of protein, ?, in a 5.3-oz serving of Chobani Flip salted caramel crunch is normally distributed with mean 12 g and standard deviation 0.7 g. A 5.3-oz serving is selected at random from the assembly line.

(a) What is the probability that there is more than 13.5 g of protein in the cup of yogurt? Give your answer to at least three decimal places.

?(?>13.5)=

(b) As part of quality control, if a randomly selected cup of yogurt contains between 11 and 13 g of protein, then the manufacturing process continues. Otherwise it is halted and inspected. If a cup of yogurt is randomly selected, what is the probability the manufacturing process is allowed to continue? What is the probability that the manufacturing process is halted and inspected? Give your answers to at least three decimal places.

?(11<?<13)=

?((?≤11)∪(?≥13))=

(c) Suppose a cup of yogurt has less than 12.5 g of protein. What is the probability that it has more than 11.5 g? Give your answer to at least three decimal places.

?(?>11.5∣?<12.5)=

(d) Suppose that six cups of yogurt are selected at random. What is the probability that at least three cups have at least 11.5 g of protein? Give your answer to at least three decimal places. The variable ? represents the number of cups out of the six randomly‑selected cups that contain at least 11.5 g of protein.

?(?≥3)=P(Y≥3)=

Answer 1

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