Student Study Guide to Accompany Statistics Alive!. Wendy J. Steinberg

      1 The distance of the score from the mean in standard deviation units and the direction of the score from the mean (either above or below).

      2 You would need to use a standardized score. Standardized scores are on the same scale, so they can be directly compared with one another.

      3 A z score tells you the location of a score in relation to the mean in standard deviation units. This is obtained by first subtracting the score from the mean (numerator). Then this deviation is scaled in standard deviation units by dividing by the distribution’s standard deviation.

      4 The mean will always be 0, and the standard deviation will always be 1.

      5 The grades are not the same in both courses because the means and standard deviations of the distributions are different. However, it does mean that your score fell in the same location relative to everyone else’s in those classes.

      1 What percentage of the normal curve falls between z = 0.64 and z = 0.89?.2389.3133.0744.9256

      2 What percentage of the normal curve falls between z = −0.93 and z = 1.60?.8238.3238.7690.4452

      3 What percentage of the normal curve falls outside the area between z = 1.5 and z = 0.34?.4338.6331.9331.3001

      4 If a distribution of scores has a mean of 15 and a standard deviation of 1.5, what is the z score for a score of 18?0.511.52

      5 The director of a new horror movie wants to know how scared her daughter was while watching the film. She asks her daughter to rate her fear on a scale of 1 to 15. If the average rating of fear for this movie is M = 6 with an SD = 0.75, where in the normal distribution would the director’s daughter’s fear level be if she gave a rating of 5?Higher than 25.23%Lower than 78.65%Higher than 9.18%Lower than 36.47%

      6 The local police department wants to determine the amount of respect that the local citizens have toward the police. They obtain data from all of the residents and find that M = 6 and SD = 1.8. In looking through the data, they notice that one participant rated his respect level at 8. What is the z score for this person?2.221.110.79−1.62

      7 What percentage of the normal curve is greater than a z of 0.34?.3669.4521.6331.7892

      8 What percentage of the normal curve falls between z = −1.2 and the mean?.0214.3849.7842.6254

      1 C

      2 C

      3 A

      4 D

      5 C

      6 B

      7 A

      8 B

      1 The raw scores of a distribution have an M = 30 and an SD = 15.1. You obtain a z score of −1.523. What is your corresponding raw score?

      2 Three electronics companies are trying to beat each other’s prices on car stereos. Here is a table with the average original prices, the standard deviations, and the current sale price of their models. Which company is offering the best deal?

      3 Two track-and-field athletes are competing to see how many first-place medals they can win during a track meet. Amanda wins seven medals; her usual winning M = 4.5, SD = 1. Ethan wins six medals; his usual winning M = 3.2, SD = 2.1. Who won more medals relative to their normal winning rates?

      4 A makeup company is attempting to lower its prices in order to improve sales. It decides to charge $5 for all of its products. If the price of eyeliner has M = $6.50 and SD = $0.35, and the price of foundation has M = $7.45 and SD = $0.78, which of these products has the bigger price reduction?

      5 A car advertisement states that its new models are able to accelerate at a rate that is 1.25 standard deviations above the mean. If the average acceleration of a car (in miles per hour) is 45 with an SD = 4.8, what is the acceleration of the car being advertised?

      6 Using the information provided in Questions 3 and 4 of Module 7’s quiz, who is the stronger student in their respective subject (Harry as a math student or Ron as an English student)? Why?

      1 7

      2 Company A

      3 Amanda

      4 Eyeliner

      5 51

      6 Harry is stronger in math than Ron is in English. Harry’s score was 2 SD above the mean in math, whereas Ron’s score was only 1.5 SD above the mean in English.