1. Several trucks arrive each day for unloading at a warehouse. An employee of the warehouse maintained for 200 days a count of the number arriving each day. This information was used to develop the probability distribution below. X P(X) 4 5 6 7 0.10 0.20 0.30 0.40 1.00 (a). Determine the expected value and the standard deviation of the number of trucks arriving each day (4+4=8 pts) 2. Suppose a life insurance company sells a $250,000 one-year term life insurance policy to a 20 -year - old female for $200. According to the National Vital Statistics Report, Vol, 53, No 6, the probability that the female survives the year is 0.999546. Compute the expected value of this policy to the insurance company. (5pts) Dr Pepper is a carbonated soft drink marketed as having a unique flavor. The drink was created in the 1880s by Charles Alderton in Waco, Texas and first served around 1885. Dr Pepper was first nationally marketed in the United States in 1904, and is now also sold in Europe, Asia, Canada, Mexico, Australia, New Zealand (as an imported drink), South Africa (also as an imported drink), and South America. Variants include a version without high fructose corn syrup, Diet Dr Pepper, as well as a line of additional flavors, first introduced in the 2000s. W.W. Clements, former CEO and president of the Dr Pepper/7-Up Company, described the taste of Dr Pepper as one-of-a-kind, saying, \"I've always maintained you cannot tell anyone what Dr Pepper tastes like because it's so different. It's not an apple, it's not an orange, it's not a strawberry, it's not a root beer, it's not even a cola. It's a different kind of drink with a unique taste all its own.\" The company currently has headquarters in Plano, Texas, and the Dr. Pepper Museum is located in Waco, Texas. [source: Wikipedia]. Of interest is the quantity of Dr Pepper, measured in ounces, that a person consumes when they drink Dr Pepper served from a fountain machine. Suppose that the quantity of Dr Pepper consumed follows an approximate normal distribution with mean 34 ounces and standard deviation 5.8 ounces. Use this information to answer questions 3 and 4. Please circle your final answers. 3. Antravious purchased a Dr Pepper fountain drink and drank 41 ounces. Based on the distribution described above, what is the probability that the quantity of Dr Pepper consumed is 41 ounces or less? 4. Shevani does not like soft drinks, and hence consumes very little Dr Pepper. Based on the distribution described above, how many ounces of Dr Pepper would a person need to consume to fall in the bottom 4.01% of the distribution? Suppose the ages of employees at the Dr Pepper Snapple Bottling Company follow an approximate normal distribution with a mean of 42.2 years and a standard deviation of 7.8 years. Use this information to answer question 5. Please circle your final answer. 5. Chnar and Rommy both work for the Dr Pepper Snapple Bottling Company; Chnar is 30 years old, while Rommy is 51 years old. Based on the distribution described above, what is the probability that the age of an employee will be between 30 and 51 years old? 6. The heights of three-year-old females are approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.A pediatrician wishes to determine the heights that separate the middle 98% of the distribution from the bottom 1% and top 1%. In other words find the 1st and the 99th percentiles