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6.1-6.2 Quiz Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) X is a normally distributed random variable with a mean of 11.00. If the probability that X is less than 11.88 is 0.67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.) A) 4.00 B) 2.40 C) 1.00 1) D) 2.00 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 2) What is the z value such that 50% of the total area under the standard normal distribution curved lies to the right of it? 2) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 3) The area under the normal distribution curve that lies within three standard deviations of the mean is approximately 95%. A) True B) False 3) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 4) Find the z value to the right of the mean so that 62.93% of the area under the distribution curve lies to the left of it. 1 4) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 5) Find the z-scores that bound the middle 74% of the area under the standard normal curve. A) -0.99, 0.99 B) -1.24, 1.24 C) -1.07, 1.07 D) -1.13, 1.13 5) 6) X is a normally distributed random variable with a mean of 4.0. Find the standard deviation of the distribution if 59.10% of the data lies to the right of 3.54. (Note: the diagram is not necessarily to scale.) 6) A) 1.3 B) 2.0 C) 1.0 D) 0.5 7) One normal curve has a mean of 24 and a standard deviation of 3. A second normal curve has a mean of 3 and a standard deviation of 24. The curve that is more dispersed, or spread out, is A) neither; by definition,a normal curve shows no spread. B) both; they are equally spread out. C) the second normal curve. D) the first normal curve. 7) 8) Find the z value that corresponds to the given area. 8) A) –0.22 B) 1.33 C) –0.51 2 D) 0.41 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 9) Stating that the area under the standard normal distribution curve between z = 0 and z = 1.00 is 0.3413, is the same as stating that the of 9) randomly selecting a standard normally distributed variable z with a value between 0 and 1.00 is 0.3413. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (mL) and standard deviation 7 mL. The fill volumes are normally distributed. What proportion of bottles have volumes greater than 999 mL? A) 0.4443 B) 0.8051 C) 1.0000 D) 0.6293 10) 11) The average hourly wage of workers at a fast food restaurant is $6.50/hr. Assume the wages are normally distributed with a standard deviation of $0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75? A) 5.2% B) 28.8% C) 42.1% D) 27.6% 11) 12) Which choice is another term that can be used to describe a normal distribution: A) bell curve B) independent variable C) negatively or positively skewed D) discrete distribution 12) 13) The number of standard deviations a particular X value is from the mean is commonly referred to as . 13) A) C) 2 B) P(X) D) z 14) A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 5 mL. The fill volumes are normally distributed. What proportion of bottles have volumes between 992 mL and 998 mL? A) 0.4207 B) 0.6452 C) 0.3399 D) 0.0808 14) 15) For a normal distribution curve with a mean of 15 and a standard deviation of 5, which range of the variable defines an area under the curve corresponding to a probability of approximately 68%? A) from 12.5 to 17.5 B) from 10 to 20 C) from 5 to 25 D) from 15 to 25 15) 3 16) A normal population has a mean = 40 and standard deviation of the population is between 24 and 32? A) 0.8408 B) 0.1592 C) 0.0735 = 11. What proportion 16) D) 0.2327 17) Identify the type of distribution pattern that occurs when the majority of the data values fall to the left of the mean? A) negatively skewed B) left skewed C) positively skewed D) symmetrical 17) 18) The area under a normal distribution curve is always positive even if the z value is negative. A) True B) False 18) 19) Find the probability P(z < 0.37) using the standard normal distribution. A) 0.6300 B) 0.1443 C) 0.3557 D) 0.6443 19) 20) On an easy test, the mean score was 96 out of a possible 100 points. The distribution of the test scores is likely to be A) symmetric. B) negatively skewed. C) diagonally skewed. D) positively skewed. 20) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 21) Mrs. Smith's reading class can read an average of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would need to read in order to get the award? Assume the data is normally distributed. 21) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 22) To find the area under the standard normal distribution curve between two z values, one first finds the difference between the two z values, then locates the value corresponding to that difference in the Standard Normal Distribution table. A) True B) False 22) 23) The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.75 miles per gallon, find the probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon. A) 0.107 B) 0.287 C) 0.273 D) 0.213 23) 4 24) The figure below is an example of a negatively skewed distribution. A) True 24) B) False 25) Find the z-score for which the area to the right is 0.27. A) 0.82 B) 0.52 C) 0.34 25) D) 0.61 26) X is a normally distributed random variable with a standard deviation of 2.00. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 10.28. (Note: the diagram is not necessarily to scale.) A) 7.5 B) 8.0 C) 9.6 26) D) 8.7 27) Find the probability P(z > -0.54) using the standard normal distribution. A) 0.7946 B) 0.2054 C) 0.2946 D) 0.7054 27) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 28) When the data values are evenly distributed about the mean, the distribution is said to be . 28) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 29) If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50. A) 6.75% B) 4.75% C) 35.54% D) 45.25% 5 29) 30) When the majority of the data values fall to the right of the mean, the distribution is said to be left-skewed. A) False B) True 30) 31) X is a normally distributed random variable with a mean of 10 and a standard deviation of 4.0. Find the value of X for which 70.54% of the area under the distribution curve lies to the right of it. (Note: the diagram is not necessarily to scale.) 31) A) 7.84 B) 8.92 C) 11.89 D) 8.56 32) Find the area under the standard normal distribution curve between z = –2.05 and z = 2.05. A) 0.9876 B) 0.9596 C) 0.4798 D) 0.4938 33) Find the z value that corresponds to the given area. A) 0.07 B) 1.23 C) 1.46 6 32) 33) D) –1.46 34) In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value? A) 0.44 B) 1.25 C) 2.10 D) 0.52 34) 35) Find the z value that corresponds to the given area. 35) A) –0.79 B) 0.57 C) 0.27 36) Find the area under the standard normal curve to the left of z = 1.5. A) 0.4332 B) 0.9332 C) 0.4666 D) 0.44 36) D) 0.0668 37) Find the probability P(0.16 < z < 1.23) using the standard normal distribution. A) 0.8271 B) 0.3600 C) 0.6729 D) 0.3271 37) 38) The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.9 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide a money-back guarantee that her 6-week poults will weigh at least a certain amount. What weight should she guarantee so that she will have to give her customer's money back only 1% of the time? A) 4.92 lb B) 3.58 lb C) 4.02 lb D) 4.47 lb 38) 39) In applied statistics, it is the area under the normal distribution curve which is most important, not the value of single points on the curve. A) True B) False 39) 40) Which of the following properties distinguishes the standard normal distribution from other normal distributions? A) The mean is 0 and the standard deviation is 1. B) The total area under the curve is equal to 1.00. C) The mean is located at the center of the distribution. D) The curve is continuous. 40) 7 41) If a normal distribution has a mean of 35 and a standard deviation of 10, then A) the median is 45 and the mode is 25. B) the median is 35 and the mode is 45. C) the median is 25 and the mode is 45. D) the median is 35 and the mode is 35. 41) 42) Find the probability P(0 < z < 1.67), using the standard normal distribution. A) 45.25% B) 42.07% C) 45.54% D) 35.54% 42) 43) X is a normally distributed random variable with a standard deviation of 3.50. Find the mean of X when 64.8% of the area lies to the left of 5.33. (Note: the diagram is not necessarily to scale.) 43) A) 3.7 B) 5.2 C) 2.1 D) 4.0 44) The normal distribution curve can be used as a probability distribution curve for normally distributed variables. A) True B) False 8 44) Answer Key Testname: 6.1-6.2 QUIZ 1) D 2) zero 3) B 4) 0.33 5) D 6) B 7) C 8) A 9) probability 10) A 11) B 12) A 13) D 14) C 15) B 16) B 17) C 18) A 19) D 20) B 21) 213 22) B 23) D 24) B 25) D 26) B 27) D 28) symmetrical 29) B 30) B 31) A 32) B 33) C 34) A 35) B 36) B 37) D 38) D 39) A 40) A 41) D 42) A 9 Answer Key Testname: 6.1-6.2 QUIZ 43) D 44) A 10