1). If the mean is greater than median and median is greater than mode for a data set, what can you conclude about the data's distribution? 2). Calculate the standard deviation for a binomial data set with the average of 28.5 and the 0.3 as probability of success? 3).You scored in the 55th percentile on the GRE. If 8,000 people took the GRE, how many people had a score at least as high as your score? 4).Use the data that is given in the following stem plot and answer questions "a" to "c" 1, 3, 2, 2, 3, 1, 2, 2, 3, 1, 0, 2, 1, 0, 3, 2, 1, 0, 3, 7, 3, 2, 1 a. Find the mode, mean and standard deviation for this data set b. Find Q1 and Q3 and represent this data using a box plot. c. What is the 40th percentile? d. Is there any outlier in this data set? Please elaborate 5). The distribution of the cars passing through a certain junction during the day follows a normal distribution with the mean value of 56 cars per hour and standard deviation of 7 cars per hour. a. What is the probability that exactly 89 cars per hour pass through that junction? b. What is the chance that the number of cars passing through that junction per hour is between 45 and 70? 6). Answerthefollowingprobabilityrelatedquestions. a)What is the relationship between events "A" and "B" if P(A)=0.45 and P(B)= 0.75 when P(A B) = 0.2 b) Calculate P(A|B) when P(A U B) = 0.76 and P(B) = 0.6 when we know A and B are complementary events. c) Calculate P(A) when P(A U B) = 0.76 and P(B) = 0.6 when we know A and B are independent events. 7). An insurance company is selling insurance to men age 85 and above. The chance that a customer survives another year is 0.95. The premium costs $2160 per year and the insurance company pays $500,000 in case the customer does not survive. a. Suppose that 8 people are insured. What is the chance that all of them survive? b. What is the expected profit/loss of the company per customer? c. How much should the premium per person be to break-even? 8). A population is repeatedly sampled with samples of size 49. The sampling distribution has an average of 28 and a standard deviation of 3.2. Calculate the average and standard deviation of the population