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Thorne and Giesen Book Cover
Statistics for the Behavioral Sciences, 4/e
Michael Thorne, Mississippi State University -- Mississippi State
Martin Giesen, Mississippi State University -- Mississippi State
The Normal Distribution

Problems

  1. Assuming that a national certification examination for a professional group has a mean score of 72 and s = 14.5, answer the following questions.

    1. What is the z score for a test score of 89.6?

    2. What is the z score for a test score of 61.5?

    3. What test score is 1.6 standard deviation units below the mean?

    4. What test score is 1.6 standard deviation units above the mean?

    5. What test scores are at least 1.5 standard deviation units away from the mean?

  2. Use Table A in Appendix 2 to answer the following questions.

    1. What is the percentage area between the mean and a z score of +0.57?

    2. What is the percentage area between the mean and a z score of –0.57?

    3. Between the mean and what z score lies approximately 46% of the normal curve? Can your answer be both positive and negative?

    4. What z score cuts off the upper 10% of the distribution?

    5. What area lies between a z score of +1.28 and a z score of +1.96?

    6. What is the area above a z score of 1.96?

    7. What is the total area between z scores of ±2.58?

    8. What is the area below a z score of –1.28?

  3. For 55 graduating seniors who took the Miller Analogies Test (MAT), the following results were obtained: ∑ X = 2,942.5, ∑ X2 = 165,606.68. Use the normal distribution to answer the following questions.

    1. What is the percentile rank of a score of 71?

    2. What is the percentile rank of a score of 35?

    3. How many seniors scored between 31 and 45?

    4. What is the score at the 95th percentile?

    5. What is the score at the 15th percentile?

    6. A university has found that scores on the MAT are highly associated with success in its graduate program in English. Specifically, seniors scoring below 41 on the test almost always fail to earn degrees, and for this reason the university will not admit a person with this score or lower. How many of the 55 seniors should not bother to apply?

    7. What MAT scores are so deviant that they occur 15% or less of the time?

    8. What MAT scores are so unlikely that they occur with a probability of .01 or less?

  4. A blood pressure testing machine is stationed in a busy corridor in a large shopping mall. For 1 week, a medical student records the diastolic pressure reading of each person who uses the machine between the hours of 10 A.M. and 2 P.M., with the following results: N = 124, ∑ X = 9,771.2, ∑ X2 = 828,360.92.

    1. How many of the sample had scores of 110 or higher?

    2. What was the probability of a score of 60 or less?

    3. If the normal range for diastolic pressures is between 60 and 90, how many of the 124 persons had a normal reading?

    4. Based on these data, what percentage of the population had readings as deviant as 110?

    5. What readings were so deviant that less than 5% of the sample had them?

  5. A national survey of speeds on interstate highways found that the average speed of 9,549 automobiles was 67.3 mph, with a standard deviation of 7.81 mph.

    1. What speed is at least 1.5 standard deviation units above the mean?

    2. How many cars from the sample of 9,549 had speeds at least 1.5 standard deviation units above the mean?

    3. What is the percentile rank of a speed of 55?

    4. What is the percentile rank of a speed of 75?

    5. How many automobiles had speeds 2 or more standard deviation units away from the mean?

    6. What speeds were so deviant that their probability of occurrence was .05 or less?

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