I need help with 4-7 only! Thank you!!

Page of4 O ZOOM + 4.) [4 points] Suppose we have a uniformly distributed random variable over the interval [16536,23 .464] . a.) What is the probability that X is within 1 standard deviation of the mean? b.) What is the probability that X is within 2 standard deviations of the mean? c.) What is the probability that X is within 3 standard deviations of the mean? d.) Does the Uniform distribution follow the Empirical Rule? Explain. Half-week 08 material: 5.) Assuming that scores on a statistics exam are normally distributed, arrange the following in ascending order: A score with a percentile rank of 76% A score at the 3\"1 quartile A score with a z-value of 0.75 Page ( > OH 6.) For each of the following uncertain quantities, discuss whether it is reasonable to assume that the probability distribution of the quantity is normal. If the answer isn't obvious, discuss how you could discover whether a normal distribution is reasonable. a.) The time it takes a bank teller to service a random customer b.) The length (in yards) of a typical drive on a par 5 by a professional golfer. c.) Your bonus from nishing a project, where your bonus is $1000 per day under the deadline if the project is completed before the deadline, your bonus is $500 if the project is completed right on the deadline, and $0 if the project is completed after the deadline. 7.) If car insurance rates for teenagers are approximately normally distributed with a standard deviation of $670 per year, nd the mean insurance rate for teenagers if 10.56% of teenagers pay more than $2,000 annually for car insurance. 8.) [6 points] Explain the mistake or misconception the students made or had in each of these problems, You do not need to solve the question, just explain what the error was. a.) Find the area under the standard normal curve to the right of 1.6 Aatit's work: 11 .6 = 0.6 :> 0.2743 0 ZOOM +