# Howard College Standard Deviations and Distribution of Scores Questions

Please do 1-40 EVEN NUMBERS and 60-676.1 The Standard Normal Distribution1. A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words. X = ____________.2. A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?3. X ~ N(1, 2)σ = _______4. A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X = ______________.5. X ~ N(–4, 1)What is the median?6. X ~ N(3, 5)σ = _______7. X ~ N(–2, 1)μ = _______8. What does a z-score measure?9. What does standardizing a normal distribution do to the mean?10. Is X ~ N(0, 1) a standardized normal distribution? Why or why not?11. What is the z-score of x = 12, if it is two standard deviations to the right of the mean?12. What is the z-score of x = 9, if it is 1.5 standard deviations to the left of the mean?13. What is the z-score of x = –2, if it is 2.78 standard deviations to the right of the mean?14. What is the z-score of x = 7, if it is 0.133 standard deviations to the left of the mean?15. Suppose X ~ N(2, 6). What value of x has a z-score of three?16. Suppose X ~ N(8, 1). What value of x has a z-score of –2.25?17. Suppose X ~ N(9, 5). What value of x has a z-score of –0.5?18. Suppose X ~ N(2, 3). What value of x has a z-score of –0.67?19. Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean?20. Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the mean?21. Suppose X ~ N(8, 9). What value of x is 0.67 standard deviations to the left of the mean?22. Suppose X ~ N(–1, 2). What is the z-score of x = 2?23. Suppose X ~ N(12, 6). What is the z-score of x = 2?24. Suppose X ~ N(9, 3). What is the z-score of x = 9?25. Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?26. In a normal distribution, x = 5 and z = –1.25. This tells you that x = 5 is ____ standard deviations to the ____ (right or left) of the mean.27. In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.28. In a normal distribution, x = –2 and z = 6. This tells you that x = –2 is ____ standard deviations to the ____ (right or left) of the mean.29. In a normal distribution, x = –5 and z = –3.14. This tells you that x = –5 is ____ standard deviations to the ____ (right or left) of the mean.30. In a normal distribution, x = 6 and z = –1.7. This tells you that x = 6 is ____ standard deviations to the ____ (right or left) of the mean.31. About what percent of x values from a normal distribution lie within one standard deviation (left and right) of the mean of that distribution?32. About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?33. About what percent of x values lie between the second and third standard deviations (both sides)?34. Suppose X ~ N(15, 3). Between what x values does 68.27% of the data lie? The range of x values is centered at the mean of the distribution (i.e., 15).35. Suppose X ~ N(–3, 1). Between what x values does 95.45% of the data lie? The range of x values is centered at the mean of the distribution(i.e., –3).36. Suppose X ~ N(–3, 1). Between what x values does 34.14% of the data lie?37. About what percent of x values lie between the mean and three standard deviations?38. About what percent of x values lie between the mean and one standard deviation?39. About what percent of x values lie between the first and second standard deviations from the mean (both sides)?40. About what percent of x values lie between the first and third standard deviations(both sides)?

Use the following information to answer the next two exercises: The life of Sunshine CD players is normally distributed with mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts.6.1 The Standard Normal Distribution

Use the following information to answer the next two exercises: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.60. What is the median recovery time?2.75.37.42.161. What is the z-score for a patient who takes ten days to recover?1.50.22.27.362. The length of time to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. If the mean is significantly greater than the standard deviation, which of the following statements is true?The data cannot follow the uniform distribution.The data cannot follow the exponential distribution..The data cannot follow the normal distribution.I onlyII onlyIII onlyI, II, and III63. The heights of the 430 National Basketball Association players were listed on team rosters at the start of the 2005–2006 season. The heights of basketball players have an approximate normal distribution with mean, µ = 79 inches and a standard deviation, σ = 3.89 inches. For each of the following heights, calculate the z-score and interpret it using complete sentences.77 inches85 inchesIf an NBA player reported his height had a z-score of 3.5, would you believe him? Explain your answer.64. The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean µ = 125 and standard deviation σ = 14. Systolic blood pressure for males follows a normal distribution.Calculate the z-scores for the male systolic blood pressures 100 and 150 millimeters.If a male friend of yours said he thought his systolic blood pressure was 2.5 standard deviations below the mean, but that he believed his blood pressure was between 100 and 150 millimeters, what would you say to him?65. Kyle’s doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean µ = 125 and standard deviation σ = 14. If X = a systolic blood pressure score then X ~ N (125, 14).Which answer(s) is/are correct?Kyle’s systolic blood pressure is 175.Kyle’s systolic blood pressure is 1.75 times the average blood pressure of men his age.Kyle’s systolic blood pressure is 1.75 above the average systolic blood pressure of men his age.Kyles’s systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure for men.Calculate

Kyle’s blood pressure.66. Height and weight are two measurements used to track a child’s development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80 cm girls in the reference population had a mean µ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N(10.2, 0.8). Calculate the z-scores that correspond to the following weights and interpret them.11 kg7.9 kg12.2 kg67. In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean µ = 520 and standard deviation σ = 115.Calculate the z-score for an SAT score of 720. Interpret it using a complete sentence.What math SAT score is 1.5 standard deviations above the mean? What can you say about this SAT score?For 2012, the SAT math test had a mean of 514 and standard deviation 117. The ACT math test is an alternate to the SAT and is approximately normally distributed with mean 21 and standard deviation 5.3. If one person took the SAT math test and scored 700 and a second person took the ACT math test and scored 30, who did better with respect to the test they took? Please compute the Mean, Median, Mode, and Standard Deviation of the data:15, 29, 26, 23, 24, 21, 16, 23, 20, 23, 24, 18, 20, 22, 23, 17, 28, 19, 21, 20, 28, 25You might want to use these links below for the computation. You may submit a screen shot of completed work

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