Refer to the Sapling Learning Normal Density Curves Interactive. The area beneath the normal density curve is separated into three regions by the values a and b. Set the mean of the normal density curve to 4.00, the standard deviation to 0.33, the zvalue of a to 3.03 and the zvalue of b to 3.03. Use the interactive to determine the area to the left of a, the area between a and b, and the area to the right of b. Sapling Learning 1.6- 1.4 - 1.2 -1 1.0- 0.8 - 0.6 - 0.4 0.2- a b 4 - 2 N . 6 Do - 10 12 14 z-value of a -1.00 Area left of a 0. 1587 x-value of a -1.00 - - - - Mean 0.00 Reset z-value of b 1.00 Area right of b 0. 1587 x-value of b 1.00 Standard 1.00 Area between a and b: 0.6826 deviation InfoSuppose a movie starts at 5:00 pm. and Lindsay, a customer who is always late, arrives at the movie theater at a random time between 5: 10 pm. and 5:45 pm. Lindsay's late arrival time, in minutes, represented by X, models a uniform distribution between 10 and 45 min. Determine the height of the uniform density curve. Provide your answer with precision to three decimal places. Calculate the probability that Lindsay is late by 15 min or less, P(X 5 15). Provide your answer with precision to three decimal places. Chobani yogurt is made using a special straining technique to remove excess liquid. This process yields a thicker, creamer yogurt with more protein per serving than a regular yogurt. Suppose the amount of protein, X, in a 53-02 serving of Chobani Flip salted caramel crunch is normally distributed with mean 12 g and standard deviation 0.7 g. A 53-02 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. (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 selcted, 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. WK) :1 P((X511)u(X213))= :1 (c) Suppose a cup of yogurt has less than 12.5 g of protein. What is the probability that is has more than 11.5 g? Give your answer to at least three decimal places. WI> ((1) 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 Y represents the number of cups out of the six randomlyselected cups that contain at least 11.5 g of protein