Task1. [5pts] The results of statistics were examined in a group of 10 students and the following data (Polish grades) were obtained: 3, 4, 3, 5, 4, 3, 3, 2, 2, 4. For the above data, build a (pointwise) distribution series (i.e. framed list of values and frequencies). Find the weighted arithmetic edian and mode. Task2 [5pts] The time X (in minutes) of the delay of 10 trains was examined and the following results were obtained: 4, 8, 4, 25, 6, 18, 20, 26, 18, 12. Calculate the arithmetic mean, median, mode and the following variation characteristics: variance, standard deviation, coefficient of variation. Task3. [5pts] The weight of a package of flour is a random variable X with the expected value m and standard deviation . 100 packages were randomly selected from the batch of flour and it was calculated that X100 = 0.998kg, S100 = 0.005kg. At the significance level a = 0.01 verify Ho(m = 1.0) vs. H(m < 1.0). Find also the critical significance level (i.e. the level acrit at which your verification decision would change). == Task4. [5pts] Feature X of the population has a normal distribution N(m,a). A 17-element sample was randomly taken from the population and the results were X17 = 19.3 and S17 = 2.5. a) At the confidence level of 0.95, find the confidence interval for the expected value m = E[X] c) At the significance level of 0.01 check the hypotheses Ho(m = 20) vs. H(m 18.5) e) At the significance level of 0.05 check the hypotheses Ho(m = 20) vs. H(m20)