1. measure of central tendency defining the quantitative average of all raw scores in a data set/sample/population; the sum of raw scores divided by the number of raw scores 2. measure of central tendency defining the midpoint of a data distribution; as many raw scores in the distribution are below this value as are above it 3. measure of central tendency defining the most commonly occurring raw score/value in a data set; distributions may have 0, 1, or more of these 4. measure of variability defining the average squared differences of raw scores in a distribution from the mean of that distribution 5. subset of a population 6. measure of variability used to determine how far raw scores in a data distribution lie from that distribution's mean. Calculated as the square root of the variance. Particularly useful measure when data exhibits normal/nearnormal distribution. It's the "sigma" in "six-sigma" statistical process control technique used in many workplace environment s. 7. graphical method for displaying the shape of a data distribution; particularly useful when the sample/data set/populatio n is large 8. tabular display showing values (or intervals of values) and the correspondin g number of times those values appear (or fall within an interval) in a distribution 9. individual piece of data ("datum") found within a data set/sample/p opulation 10. symbol & variable representing the sum of raw scores in a data set / data distribution 11. variable representing the number of raw scores in a data set / data distribution Question 4 (5 points) A survey of 15 randomly selected students responded to the question \"How many hours a day do you work on MATH 106?\" as follows: 3, 2, 2, 4, 6, 5, 2, 5, 1, 4, 2, 3, 2, 3, 4 . Which histogram above accurately reflects the frequency distribution of the 15 students' responses? Question 4 options: Histogram A Histogram C Histogram D Histogram B Question 5 (5 points) In a histogram, when the data are symmetrical, what is the typical relationship between the mean and median? Question 5 options: A) Value of mean is greater than value of median (mean > median) B) Value of mean is approximately the same as the value of median (mean median) C) Value of mean is less than value of median (mean < median) D) There's no relationship between the mean and median of a data distribution Question 6 (5 points) Question 6 options: The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200. For these six salaries, find: a. the mean Enter answer in dollars rounded to the nearest cent. Do NOT enter "$" sign in answer. b. the median Enter answer in dollars rounded to the nearest cent. Do NOT enter "$" sign in answer c. the mode(s) (if it.they exist) Enter answer in dollars rounded to the nearest cent. Do NOT enter "$" sign in answer. If no mode exists, enter NONE . If more than one mode exists, enter mode values separated by comma (no spaces) Question 7 (5 points) Question 7 options: Calculate for the following data set: 1; 1; 1; 2; 2; 2; 2; 3; 3; 3; 3; 3; 3; 3; 3; 4; 4; 4; 5; 5 a. the mean Enter answer rounded to the nearest hundredth (two places after decimal) b. the median Enter answer rounded to the nearest hundredth (two places after decimal) c. the mode(s) (if it.they exist) Since all raw scores in data set are whole numbers, enter answer as a whole number. If no mode exists, enter NONE . If more than one mode exists, enter mode values separated by comma (no spaces) Question 8 (5 points) Question 8 options: Calculate for the following data set: 87; 87; 87; 87; 87; 88; 89; 89; 90; 91 a. the mean Enter answer rounded to the nearest hundredth (two places after decimal) b. the median Enter answer rounded to the nearest hundredth (two places after decimal) c. the mode(s) (if it.they exist) Since all raw scores in data set are whole numbers, enter answer as whole number. If no mode exists, enter NONE . If more than one mode exists, enter mode values separated by comma (no spaces) Question 9 Question 14 (7.5 points) Question 14 options: The probability of \"heads\" coming face-up on a single flip of a fair two-sided coin is 0.5. You flip the coin a total of ten (10) times. What is the probability of getting exactly 7 \"heads\" in those 10 flips? Enter answer response as probability rounded to nearest ten-thousandth (four places after decimal). Examples of correctly entered responses: 0.0031 0.0450 0.2593 0.7000 1.0000 Question 15 (7.5 points) Question 15 options: The probability that you will win a certain game is 0.3. If you play the game 20 times, what is the probability that you will win 3 or fewer times? Enter answer response as probability rounded to nearest ten-thousandth (four places after decimal). Examples of correctly entered responses: 0.0031 0.0450 0.2593 0.7000 1.0000 Question 16 (7.5 points) Question 16 options: One of the initial clinical trials of the anti-math anxiety drug SHOVITALL tested for the presence of headaches as a side effect. In the trial, 450 subjects were treated with 80mg of the drug, and 2.2% of the subjects developed headaches. In the binomial distribution of these 450 subjects, using p = = 0.022, find: a. the population mean Enter answer rounded to the nearest tenth (one place after decimal). Examples of correctly entered responses: 0.0 0.3 4.7 13.5 b. the population standard deviation Enter answer rounded to the nearest ten-thousandth (four places after decimal). Examples of correctly entered responses: 0.0000 0.3050 4.7320 13.5172 Question 1 (5 points) For a normal distribution with mean of 100 and a standard deviation of 12, find the number of standard deviations the raw score 76 is from the mean. Enter answer as a positive value rounded to nearest hundredth (two places after decimal). Question 1 options: Question 2 (5 points) For a normal distribution with mean of 80 and a standard deviation of 8, find the number of standard deviations the raw score 67 is from the mean. Enter answer as a positive value rounded to nearest hundredth (two places after decimal). Question 2 options: Question 3 (5 points) Question 3 options: A normal distribution has a mean of 40 and a standard deviation of 5. 68% of the distribution (centered about the mean) can be found between raw scores: Enter answers rounded to nearest integer. Examples of correctly-entered responses: -11 and 0 27 Question 4 (5 points) Question 4 options: A normal distribution has a mean of 5 and a standard deviation of 2. What proportion of the distribution is above 3? Click on link Normal Distribution Area Calculator to calculate answer Enter answer rounded to the nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0000 0.0076 0.1500 0.3000 0.5429 1.0000 Question 5 (5 points) Question 5 options: A normal distribution has a mean of 12 and a standard deviation of 3. What proportion of the distribution is below 7? Click on link Normal Distribution Area Calculator to calculate answer Enter answer rounded to the nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0000 0.0076 0.1500 0.3000 0.5429 1.0000 Question 6 (5 points) Question 6 options: A normal distribution of test scores has a mean of 38 and a standard deviation of 6. Everyone scoring at or above the 80th percentile gets placed in an advanced class. What is the cutoff score to get into the class? Click on link Inverse Normal Distribution Area Calculator to calculate answer Enter answer rounded to the nearest hundredth (2 places after decimal). Examples of correctly entered responses: 0.84 12.03 20.50 76.18 100.00 Question 7 (5 points) Question 7 options: A normal distribution has a mean of 120 and a variance of 100. 35% of the area is below what number? Click on link Inverse Normal Distribution Area Calculator to calculate answer Enter answer rounded to the nearest hundredth (2 places after decimal). Examples of correctly entered responses: 0.84 12.03 20.50 76.18 Question 8 (2.5 points) 100.00 A normal distribution is said to be a standard normal distribution when: Question 8 options: A) its mean = 0 and its standard deviation = 1 B) its mean = 1 and its standard deviation = 1 C) its mean = 1 and its standard deviation = 0 D) its mean = its standard deviation, regardless of the value Question 9 (2.5 points) The "total area" under the "curve" (the "bell curve") of a standard normal distribution is ALWAYS equal to: Question 9 options: A) value of mean plus one std deviation B) value of mean C) 1 D) value of one standard deviation Question 10 (5 points) Question 10 options: A normal distribution has a mean of 100 and a standard deviation of 10. What is the Z score that corresponds with 78? Enter answer rounded to nearest hundredth (two places after decimal) with "+" or "-" sign in front (no spaces between sign and number value of answer). Examples of correctly entered responses: +2.21 -3.10 -0.45 +1.00 Question 11 (5 points) Question 11 options: A normal distribution has a mean of 75 and a standard deviation of 15. What is the raw score that corresponds with a Z score of 1.6? Enter answer rounded to nearest hundredth (two places after decimal). Examples of correctly entered responses: 3.75 12.04 41.33 97.00 Question 12 (5 points) Question 12 options: A normal distribution has a mean of 200 and a standard deviation of 25. What is the raw score that corresponds with a Z score of -1.5? Enter answer rounded to nearest hundredth (two places after decimal). Examples of correctly entered responses: 3.75 12.04 41.33 97.00 Question 13 (5 points) Question 13 options: A normal distribution has a mean of 18 and a standard deviation of 5. Use the link Normal Distribution Area Calculator to determine the proportion of the raw scores (area) below raw score of 6. Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 14 (5 points) Question 14 options: Find the area under the standard normal curve from a Z score = - 2.5 to Z = 0. Use the link Normal Distribution Area Calculator to determine the area. Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 15 (7.5 points) Question 15 options: The original Stanford-Binet intelligence quotient tests measured a person's IQ using a normal distribution with a mean of 100 and a standard deviation of 10. a. What is the Z score that corresponds with a raw score of 122? Enter answer rounded to nearest hundredth (two places after decimal) with "+" or "-" sign in front (no spaces between sign and number value of answer). Examples of correctly entered responses: +2.21 -3.10 -0.45 +1.00 b. Find the area under the standard normal curve from the mean to the raw score of 122. Use the link Normal Distribution Area Calculator to determine the area. Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 16 (7.5 points) Question 16 options: \"Cut-It-Up\" brand chain saws have an average service life of 120 months with a standard deviation of 15 months. Assuming a normal distribution, find the probability that a \"Cut-It-Up\" chain saw will last for more than 140 months. Compute Z score and use the link Normal Distribution Area Calculator to compute the corresponding probability (the "area under the curve"). Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 17 (7.5 points) Question 17 options: The average healing time from a particular inpatient surgical procedure is 200 hours, with a standard deviation of 20 hours. What percentage of the people having this surgical procedure will heal in 170 hours or less? Compute Z score and use the link Normal Distribution Area Calculator to compute the corresponding probability (the "area under the curve"). Remember: probability (as a decimal) x 100 = probability as a percentage. Enter answer as a percentage rounded to nearest hundredth (2 places after decimal). Do NOT enter "%" sign with answer. Examples of correctly entered responses: 0.00 0.70 3.12 37.05 100.00 Question 18 (5 points) Which of the following statements are NOT true concerning the use of a normal distribution to approximate a binomial distribution? Question 18 options: A) Approximation is adequate if, for n number of trials and probability of success , both (n) and (n)(1-) are values greater than 10 B) Binomial distributions are discrete probability distributions, while normal distributions are continuous probability distributions C) All these distractor statements are true. D) A normal distribution can be used to determine the exact probability of getting exactly 8 "heads" in 10 flips of a fair two-sided coin Question 19 (7.5 points) Question 19 options: You decide to use the normal distribution to approximate the binomial distribution. You want to know the probability of getting from 7 to 13 heads out of 20 flips of a fair, two - sided coin. Use = 0.5 (a coin flip is a 50-50 shot, right?). a. Find the mean of the normal distribution Enter answer rounded to the nearest hundredth (two places after decimal) b. Find the standard deviation of the normal distribution Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0000 0.0103 0.2500 0.6751 1.0000 c. Using the mean and standard deviation you calculated, compute Z scores and use the link Normal Distribution Area Calculator to compute the corresponding probability (the "area under the curve"). Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 1 (5 points) For a normal distribution with mean of 100 and a standard deviation of 12, find the number of standard deviations the raw score 76 is from the mean. Enter answer as a positive value rounded to nearest hundredth (two places after decimal). Question 1 options: Question 2 (5 points) For a normal distribution with mean of 80 and a standard deviation of 8, find the number of standard deviations the raw score 67 is from the mean. Enter answer as a positive value rounded to nearest hundredth (two places after decimal). Question 2 options: Question 3 (5 points) Question 3 options: A normal distribution has a mean of 40 and a standard deviation of 5. 68% of the distribution (centered about the mean) can be found between raw scores: Enter answers rounded to nearest integer. Examples of correctly-entered responses: -11 and 0 27 Question 4 (5 points) Question 4 options: A normal distribution has a mean of 5 and a standard deviation of 2. What proportion of the distribution is above 3? Click on link Normal Distribution Area Calculator to calculate answer Enter answer rounded to the nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0000 0.0076 0.1500 0.3000 0.5429 1.0000 Question 5 (5 points) Question 5 options: A normal distribution has a mean of 12 and a standard deviation of 3. What proportion of the distribution is below 7? Click on link Normal Distribution Area Calculator to calculate answer Enter answer rounded to the nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0000 0.0076 0.1500 0.3000 0.5429 1.0000 Question 6 (5 points) Question 6 options: A normal distribution of test scores has a mean of 38 and a standard deviation of 6. Everyone scoring at or above the 80th percentile gets placed in an advanced class. What is the cutoff score to get into the class? Click on link Inverse Normal Distribution Area Calculator to calculate answer Enter answer rounded to the nearest hundredth (2 places after decimal). Examples of correctly entered responses: 0.84 12.03 20.50 76.18 100.00 Question 7 (5 points) Question 7 options: A normal distribution has a mean of 120 and a variance of 100. 35% of the area is below what number? Click on link Inverse Normal Distribution Area Calculator to calculate answer Enter answer rounded to the nearest hundredth (2 places after decimal). Examples of correctly entered responses: 0.84 12.03 20.50 76.18 Question 8 (2.5 points) 100.00 A normal distribution is said to be a standard normal distribution when: Question 8 options: A) its mean = 0 and its standard deviation = 1 B) its mean = 1 and its standard deviation = 1 C) its mean = 1 and its standard deviation = 0 D) its mean = its standard deviation, regardless of the value Question 9 (2.5 points) The "total area" under the "curve" (the "bell curve") of a standard normal distribution is ALWAYS equal to: Question 9 options: A) value of mean plus one std deviation B) value of mean C) 1 D) value of one standard deviation Question 10 (5 points) Question 10 options: A normal distribution has a mean of 100 and a standard deviation of 10. What is the Z score that corresponds with 78? Enter answer rounded to nearest hundredth (two places after decimal) with "+" or "-" sign in front (no spaces between sign and number value of answer). Examples of correctly entered responses: +2.21 -3.10 -0.45 +1.00 Question 11 (5 points) Question 11 options: A normal distribution has a mean of 75 and a standard deviation of 15. What is the raw score that corresponds with a Z score of 1.6? Enter answer rounded to nearest hundredth (two places after decimal). Examples of correctly entered responses: 3.75 12.04 41.33 97.00 Question 12 (5 points) Question 12 options: A normal distribution has a mean of 200 and a standard deviation of 25. What is the raw score that corresponds with a Z score of -1.5? Enter answer rounded to nearest hundredth (two places after decimal). Examples of correctly entered responses: 3.75 12.04 41.33 97.00 Question 13 (5 points) Question 13 options: A normal distribution has a mean of 18 and a standard deviation of 5. Use the link Normal Distribution Area Calculator to determine the proportion of the raw scores (area) below raw score of 6. Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 14 (5 points) Question 14 options: Find the area under the standard normal curve from a Z score = - 2.5 to Z = 0. Use the link Normal Distribution Area Calculator to determine the area. Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 15 (7.5 points) Question 15 options: The original Stanford-Binet intelligence quotient tests measured a person's IQ using a normal distribution with a mean of 100 and a standard deviation of 10. a. What is the Z score that corresponds with a raw score of 122? Enter answer rounded to nearest hundredth (two places after decimal) with "+" or "-" sign in front (no spaces between sign and number value of answer). Examples of correctly entered responses: +2.21 -3.10 -0.45 +1.00 b. Find the area under the standard normal curve from the mean to the raw score of 122. Use the link Normal Distribution Area Calculator to determine the area. Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 16 (7.5 points) Question 16 options: \"Cut-It-Up\" brand chain saws have an average service life of 120 months with a standard deviation of 15 months. Assuming a normal distribution, find the probability that a \"Cut-It-Up\" chain saw will last for more than 140 months. Compute Z score and use the link Normal Distribution Area Calculator to compute the corresponding probability (the "area under the curve"). Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000 Question 17 (7.5 points) Question 17 options: The average healing time from a particular inpatient surgical procedure is 200 hours, with a standard deviation of 20 hours. What percentage of the people having this surgical procedure will heal in 170 hours or less? Compute Z score and use the link Normal Distribution Area Calculator to compute the corresponding probability (the "area under the curve"). Remember: probability (as a decimal) x 100 = probability as a percentage. Enter answer as a percentage rounded to nearest hundredth (2 places after decimal). Do NOT enter "%" sign with answer. Examples of correctly entered responses: 0.00 0.70 3.12 37.05 100.00 Question 18 (5 points) Which of the following statements are NOT true concerning the use of a normal distribution to approximate a binomial distribution? Question 18 options: A) Approximation is adequate if, for n number of trials and probability of success , both (n) and (n)(1-) are values greater than 10 B) Binomial distributions are discrete probability distributions, while normal distributions are continuous probability distributions C) All these distractor statements are true. D) A normal distribution can be used to determine the exact probability of getting exactly 8 "heads" in 10 flips of a fair two-sided coin Question 19 (7.5 points) Question 19 options: You decide to use the normal distribution to approximate the binomial distribution. You want to know the probability of getting from 7 to 13 heads out of 20 flips of a fair, two - sided coin. Use = 0.5 (a coin flip is a 50-50 shot, right?). a. Find the mean of the normal distribution Enter answer rounded to the nearest hundredth (two places after decimal) b. Find the standard deviation of the normal distribution Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0000 0.0103 0.2500 0.6751 1.0000 c. Using the mean and standard deviation you calculated, compute Z scores and use the link Normal Distribution Area Calculator to compute the corresponding probability (the "area under the curve"). Enter answer rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered responses: 0.0001 0.0034 0.0501 0.7849 1.0000