. Question 2 > 0/1 pt 9 3 99 0 Details The average time to run the 5K fun run is 23 minutes and the standard deviation is 2.5 minutes. 48 runners are randomly selected to run the 22 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N b. What is the distribution of x? X ~ N( C. What is the distribution of a? > x - N d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.1588 and 23.5588 minutes. e. For the 48 runners, find the probability that their average time is between 23.1588 and 23.5588 minutes. f. Find the probability that the randomly selected 48 person team will have a total time more than 1123.2. g. For part e) and f), is the assumption of normal necessary? O YesO No h. The top 20% of all 48 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes Question 3 v & 0/1 pt 3 299 @ Details Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 47 minutes and standard deviation 23 minutes. A researcher observed 6 students who entered the library to study. Round all answers to 4 decimal places where possible. Q N =h . What is the distribution of X? X ~ N( , ) . What is the distribution of Z? ~ N( , ) .What is the distribution of 2?2 & ~ N( , ) . If one randomly selected student is timed, find the probability that this student's time will be between 42 and 50 minutes. . For the 6 students, find the probability that their average time studying is between 42 and 50 minutes. . Find the probability that the randomly selected 6 students will have a total study time less than 324 minutes. . For part e) and f), is the assumption of normal necessary? NoO Yes . The top 10% of the total study time for groups of 6 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? minutes Question 5 v & 0/1 pt 3 299 @ Details The average amount of money that people spend at Don Mcalds fast food place is $7.8600 with a standard deviation of $1.5400. 11 customers are randomly selected. Please answer the following qguestions, and round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N( , ) b. What is the distribution of ? ~ N( , ) c. What is the distribution on x? Z x ~ N( , ) d. What is the probability that one randomly selected customer wiill spend less than $7.8536? e. For the 11 customers, find the probability that their average spent is more than $7.8536. f. Find the probability that the randomly selected 11 customers will spend less than $86.3896. g. For part e) and f), is the assumption of normal necessary? O YesO No h. The owner of Don Mcalds gives a coupon for a free sundae to the 3% of all groups of 11 people who spend the most money. At least how much must a group of 11 spend in total to get the free sundae? $ Question 6 vl| & 0/1pt 3 299 @ Details The average score for games played in the NFL is 20.8 and the standard deviation is 9.2 points. 43 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of Z? T ~ N( , ) b. What is the distribution of Z x? Z x ~ N( , ) c. P(z > 21.7955) = d. Find the 76th percentile for the mean score for this sample size. e. P(20.3955