3.

When a student performs poorly on a midterm exam, the student sometimes is convinced that their score is an anomaly and that they will do much better on the final exam. The data below show the midterm and final scores (out of 100 points) for eight students in an introductory statistics class. Student Midterm Final 1 70 88 58 52 85 84 4 82 74 70 80 6 40 36 7 85 48 8 85 96 a) Construct a scatterplot for the data. Describe the pattern that you see in the scatterplot. Are there any clusters or outliers? If so, how would you explain them? b) Calculate the regression line for predicting a student's score on the final exam based on the student's score on the midterm.The daily yield for a local chemical plant has averaged 880 tons for the last several years. The quality control manager would like to know whether this average has changed in recent months. She randomly selects 50 days from the computer database and computes the average and standard deviation of the n = 50 yields as x = 871 tons and s = 21 tons, respectively. Test the appropriate hypothesis using a = .05.The number of times x an adult human breathes per minute when at rest has a probability distribution that is approximately normal, with the mean equal to 16 and the standard deviation equal to 4. If a person is selected at random and the number x of breaths per minute while at rest is recorded, what is the probability that x will exceed 22