Can I please have a detailed explanation on these?

I) On the planet of Mercury, 4-year-olds average 2.9 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( b. Find the probability that the child spends less than 2.1 hours per day unsupervised. c. What percent of the children spend over 4.4 hours per day unsupervised. ' -% (Round to 2 decimal places) d. 74% of all children spend at least how many hours per day unsupervised? hours. L The average THC content of marijuana sold on the street is 10.5%. Suppose the THC content is normally distributed with standard deviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. 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 bag of marijuana sold on the street will have a THC content greater than 12.1. ' c. Find the 72nd percentile for this distribution. ' I96 3) Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 4 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( b. If one of the trials is randomly chosen, find the probability that it lasted at least 19 days. c. If one of the trials is randomly chosen, find the probability that it lasted between 25 and 30 days. d. 77% of all of these types of trials are completed within how many days? (Please enter a whole number) (DThe average number of words in a romance novel is 64,043 and the standard deviation is 17,442. 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(' I; b. Find the proportion of all novels that are between 48,345 and 65,787 words. I c. The 70th percentile for novels is I words. (Round to the nearest word) d. The middle 70% of romance novels have from I Iwords toI words. {Round to the nearest word) Los Angeles workers have an average commute of 28 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 14 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible. I 5 a. What is the distribution of X? X ~ N( b. Find the probability that a randomly selected LA worker has a commute that is longer than 34 minutes. c. Find the 85th percentile for the commute time of LA workers. minutes 6) On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 102 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X ~ N{ I) b. Find the probability that a randomly selected person's IQ is over 95. I Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 7% for 1Q scores. What is the highest IQ score a child can have and still receive special services? IRound your answer to 2 decimal places. (I. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: I I Q3: I I IQR: I I Hints: . We write X ~ N(u,6) to mean that the distribution is Normal (N) with mean u and standard deviation o. The mean and the standard deviation are given in the problem. . For a normal distribution, the mean and the median are the same. . To find the z-score, use the formula: z = (x - H)/6. . To find the probability that an event is between two numbers a and b, use your calculator with N(a, b, M,5). . To find the probability that an event is less than a number a, use your calculator with N(-99999,a,u,). It is recommended that you use at least enough 9's so that the lower bound is at least 10 times larger in magnitude than the maximum magnitude of a, H, and o. . To find the probability that an event is greater than a number b, use your calculator with N(b,99999,u,). It is recommended that you use at least enough 9's so that the upper bound is at least 10 times larger in magnitude than the maximum of b, u, and 5 . . For normal distribution probabilities, _ is the same as is the same as >. . If you want to find the value such that the proportion of the data that is below that value is p, then use the inverse normal: invNorm(p,H,G). . To find the p percentile, first convert p to a decimal and then use the inverse normal. For example, to find the 17th percentile, use invNorm(0.17,u,). Note that the first quartile is the 25th percentile and the third quartile is the 75th percentile. . To find out the value such that the proportion above that value is p, first subtract from 1 and then use the hint above. invNorm(1-p,M,6)