# Normal Distribution

Pages: 7 (2715 words) Published: February 5, 2012
Final Exam Review Questions Solutions Guide You will probably want to PRINT THIS so you can carefully check your answers. Be sure to ask your instructor if you have questions about any of the solutions given below. 1. Explain the difference between a population and a sample. In which of these is it important to distinguish between the two in order to use the correct formula? mean; median; mode; range; quartiles; variance; standard deviation. Solution: A sample is a subset of a population. A population consists of every member of a particular group of interest. The variance and the standard deviation require that we know whether we have a sample or a population. 2. The following numbers represent the weights in pounds of six 7year old children in Mrs. Jones' 2nd grade class. {25, 60, 51, 47, 49, 45} Find the mean; median; mode; range; quartiles; variance; standard deviation. Solution: mean = 46.166.... median = 48 mode does not exist range = 35 Q1 = 45 Q2 = median = 48 Q3 = 51 variance = 112.1396 standard deviation =10.59 3. If the variance is 846, what is the standard deviation? Solution: standard deviation = square root of variance = sqrt(846) = 29.086 4. If we have the following data

34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66 Draw a stem and leaf. Discuss the shape of the distribution. Solution: 2 3 4 5 6 | | | | | 219200 48714 0197 6

This distribution is right skewed (positively skewed) because the “tail” extends to the right. 5. What type of relationship is shown by this scatter plot? 45 40 35 30 25 20 15 10 5 0 0 5 10 15 20

Solution: Weak positive linear correlation 6. What values can r take in linear regression? Select 4 values in this interval and describe how they would be interpreted. Solution: the values are between –1 and +1 inclusive. -1 means strong negative correlation +1 means strong positive correlation 0 means no correlation .5 means moderate positive correlation etc. 7. Does correlation imply causation? Solution: No.

8. What do we call the r value. Solution: The correlation coefficient. 9. To predict the annual rice yield in pounds we use the equation ˆ y = 859 + 5.76 x1 + 3.82 x2 , where x1 represents the number of acres planted (in thousands) and where x2 represents the number of acres harvested (in thousands) and where r2 = .94. a) Predict the annual yield when 3200 acres are planted and 3000 are harvested. b) Interpret the results of this r2 value. c) What do we call the r2 value? Solution: ˆ (a) y = 859 + 5.76*3200 + 3.82*3000 = 859 + 18432 + 11460 = 30751 which is 30,751,000 pounds of rice (b) 94% of the variation in the annual rice yield can be explained by the number of acres planted and harvested. The remaining 6% is unexplained and is due to other factors or to chance. (c) It is the coefficient of determination. 10. The Student Services office did a survey of 500 students in which they asked if the student is part-time or full-time. Another question asked whether the student was a transfer student. The results follow. Transfer Non-Transfer Row Totals Part-Time Full-Time 100 170 110 120 230 210 290 500

Column Totals 270

a) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student. P (Transfer) b) If a student is selected at random (from this group of 500 students), find the probability that the student is a part time student. P (Part Time) c) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student and a part time student. P(transfer ∩ part time).

d) If a student is selected at random (from this group of 500 students), find the probability that the student is a transfer student if we know he is a part time student. P(transfer | part time). e) If a student is selected at random (from this group of 500 students), find the probability that the student is a part time given he is a transfer student. P(part time |...