A sample of ?=14n=14 observations is drawn from a normal population with ?=1030μ=1030 and ?=200σ=200. Find each of the following: A. ?(?¯>1110)P(X¯>1110) Probability =  B. ?(?¯<944)P(X¯<944) Probability =  C. ?(?¯>997)P(X¯>997) Probability =

Find the probability that the mean for 20 randomly selected distances is greater than 195.70 cm.

A rare form of malignant tumor occurs in 11 children in a​ million, so its probability is 0.000011. Four cases of this tumor occurred in a certain​ town, which had 14,318 children. Assuming that this tumor occurs as​ usual, find the mean number of cases in groups of 14,318 children. Using the unrounded mean from part (a​), find the probability that the number of tumor cases in a group of 14,318 children is 0 or 1. What is the probability of more than one​ case? Does the cluster of four cases appear to be attributable to random​ chance? Why or why​ not? (*Need before midnight pleeeease!)

A sample of 30 students at a local college were given a test consisting of 10 questions about current news events. Thedistribution of the number of correct answers given is recorded in the frequency column of the table. Questions that were notanswered were marked incorrect. The frequency represents how many of the 30 students who took the test got a certain numberof answers correct. For example, three students answered five questions correctly. Determine this mean number of points x, earned on the test. Give your answer precise to one decimal place