I need help with these 9 questions please

1.

The highest grade for Florida oranges is U.S. Fancy and is based principally on color. Suppose that Shannon owns a small organic orchard and that the proportion of oranges she grows which can be classied as U.S. Fancy is 0.40. One morning, Shannon randomly picks 44 oranges. Estimate the probability that the number of oranges that will be classied as U.S. Fancy, X, is fewer than 16. Use a normal approximation to the binomial distribution with continuity correction to obtain the solution. Give your answer precise to at least four decimal places. Sapling Learning 1.6- 1.4- 1.2 - 1.0- 0.8- 0.6- 0.4 0.2 - a b 4 - 2 N- 6 8 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 InfoRefer 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. According to the College Board, SAT mathematics scores from the 2014 school year for high school students in the United States were normally distributed with a mean of 513 and a standard deviation of 120. Use a standard normal table such as this one to determine the probability that a randomly chosen high school student who took the SAT in 2014 will have a mathematics SAT score between 400 and 750 points. Give your answer as a percentage rounded to one decimal place. MC] Neil is a drummer who purchases his drumsticks online. When practicing with the newest pair, he notices they feel heavier than usual. When he weighs one of the sticks, he nds that it is 2.23 oz. The manufacturer's website states that the average weight of each stick is 1.85 oz with a standard deviation of 0.18 oz. Assume that the weight of the drumsticks is normally distributed. What is the probability of the stick's weight being 2.23 oz or greater? Give your answer as a percentage precise to at least two decimal places. You might nd this table of standard normal critical values useful. :M Suppose that a random variable Z has a standard normal distribution. Find a such that P(Z > a) = 0.151. Give your answer to two decimal places. You may find this Z-table useful. a =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 5.3-oz serving of Chobani Flip salted caramel crunch is normally distributed with mean 12 g and stande deviation 0.7 g. A 5302 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. W) P((X211)U(X213))= :] (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. W...) [:1 ((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. Suppose Gabe, an elementary school student, has just nished dinner with his mother, Judy. Eyeing the nearby cookie jar, Gabe asks his mother if he can have a cookie for dessert. She tells Gabe that she needs to check his backpack to make sure that he nished his homework. Gabe cannot remember where he left his backpack, but he knows for sure that he did not complete his homework and will not be allowed to eat a cookie. Gabe believes his only option is to quickly steal a cookie while his mother is out of the room. Judy then leaves the room to look for Gabe's backpack. Assume that Judy could return at any time in the next 90 seconds with equal probability. For the rst 40 seconds, Gabe sheepishly wonders if he will get caught trying to grab a nearby cookie. After waiting and not seeing his mother, Gabe decides that he needs a cookie and begins to take one from the jar. Assuming it takes Gabe 30 seconds to grab a cookie from the jar and devour it without a trace, what is the probability that his mother returns in time to catch Gabe stealing a cookie? Please round your answer to the nearest two decimal places. P(Gabe gets caught) = C] Suppose 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 S 15). Provide your answer with precision to three decimal places. A simple random sample of 90 analog circuits is obtained at random from an ongoing production process in which 25% of all circuits produced are defective. Let X be a binomial random variable corresponding to the number of defective circuits in the sample. Use the normal approximation to the binomial distribution to compute P (19 S X S 28), the probability that between 19 and 28 circuits in the sample are defective. Report your answer to two decimal places of precision