The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2781 and standard deviation 500. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. Find the probability that the customer consumes less than 2516 calories. c. What proportion of the customers consume over 2908 calories?
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- The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 64 minutes and a standard deviation of 16 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 79 minutes. c. The park service is considering offering a discount for the 8% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutesThe average number of words in a romance novel is 64,387 and the standard deviation is 17,436. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. Find the proportion of all novels that are between 48,695 and 66,131 words. c. The 95th percentile for novels is words. (Round to the nearest word) d. The middle 80% of romance novels have from words to words. (Round to the nearest word)The average number of words in a romance novel is 64,159 and the standard deviation is 17,401. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(__________ , ___________) b. Find the proportion of all novels that are between 50,238 and 58,939 words. _______________c. The 85th percentile for novels is_____________________ words. (Round to the nearest word)d. The middle 60% of romance novels have from ______________ words to ________________words. (Round to the nearest word)
- On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 117 and a standard deviation of 14. Suppose one individual is randomly chosen. Let X = IQ of an individual.b. Find the probability that a randomly selected person's IQ is over 108. Round your answer to 4 decimal places.c. A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places.Q1: Q3: IQR:The average score of all golfers for a particular course has a mean of 61 and a standard deviation of 5. Suppose 100 golfers played the course today. Find the probability that the average score of the 100 golfers exceeded 62. Round to four decimal places. O A. 0.1293 B. 0.3707 O C. 0.4772 O D. 0.0228The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 60 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 81 minutes. c. The park service is considering offering a discount for the 7% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes
- The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 64 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 57 minutes. c. The park service is considering offering a discount for the 7% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutesThe average number of words in a romance novel is 64,177 and the standard deviation is 17,405. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(____, ______)b. Find the proportion of all novels that are between 48,512 and 60,696 words. _________?c. The 95th percentile for novels is words. (Round to the nearest word)_________?d. The middle 60% of romance novels have from______ words to ______words. (Round to the nearest word)The average production cost for major movies is 57 million dollars and the standard deviation is 20 million dollars. Assume the production cost distribution is normal. Suppose that 46 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 57 20 b. What is the distribution of ? - N c. For a single randomly selected movie, find the probability that this movie's production cost is between 52 and 55 million dollars. 58 d. For the group of 46 movies, find the probability that the average production cost is between 52 and 55 million dollars. e. For part d), is the assumption of normal necessary? Yes No
- The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 74 minutes and a standard deviation of 17 minutes. Suppose one person at the hot springs is randomly chosen. Let X - the amount of time that person spent at Grover Hot Springs. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N b. Find the probability that a randomly selected person at the hot springs stays longer then 85 minutes. c. The park service is considering offering a discount for the 4% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (1QR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes6. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 210 feet and a standard deviation of 50 feet. Let X = distance in feet for a fly ball. Write the probability statement. (Let k represent the score that corresponds to the 80th percentile.) 80th percentile: 252.1 ftThe amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 63 minutes and a standard deviation of 15 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. Find the probability that a randomly selected person at the hot springs stays longer then 68 minutes. C. The park service is considering offering a discount for the 4% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes