STAT 1600 - normal definitions solutions. Questions and Answers

STAT 1600 - normal definitions solutions. Questions and Answers STAT1600 Statistics : Ideas & Concepts Example class 3 - ANSWERS 1. Answer true or false for the following: (a) The Z scores can be used to identify outliers. ANSWER: True (b) The larger the Z score, the further is the distance from the observation to the median. ANSWER: False (c) As a general rule, an observation is considered an extreme value if its Z score is greater than -3. ANSWER: False (d) As a general rule, an observation is considered an extreme value if its Z score is greater than 3. ANSWER: True (e) As a general rule, an observation is considered an extreme value if its Z score is less than 3. ANSWER: False (f) As a general rule, an observation is considered an extreme value if its Z score is less than -3. ANSWER: True (g) The Z score of an observation can never be negative. ANSWER: False (h) The Z score of an observation measures how many standard deviations the value is from the mean. ANSWER: True 2. Answer the following multiple choice questions. (a) In its standardized form, the normal distribution (A) has a mean of 0 and a standard deviation of 1. * (B) has a mean of 1 and a variance of 0. (C) has an area equal to 0.5. (D) cannot be used to approximate discrete probability distributions. (b) Which of the following about the normal distribution is not true? (A) Theoretically, the mean, median, and mode are the same. (B) About 2/3 of the observations fall within 1 standard deviation from the mean. (C) It is a discrete probability distribution. * (D) Its parameters are the mean and variance. (c) If a particular batch of data is approximately normally distributed, we would find that approximately (A) 2 of every 3 observations would fall between 1 standard deviation around the mean. (B) 4 of every 5 observations would fall between 1.28 standard deviations around the mean. (C) 19 of every 20 observations would fall between 2 standard deviations around the mean. (D) All of the above. * (d) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. The value of Z is (A) 0.18 (B) 0.81 (C) 1.16 * (D) 1.47 (e) For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3340. The value of Z is (A) 0.07 (B) 0.37 (C) 0.97 * (D) 1.06 (f) For some value of Z, the probability that a standard normal variable is below Z is 0.2090. The value of Z is (A) - 0.81 * (B) - 0.31 (C) 0.31 (D) 1.96