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- 2. A statistic test has a mean of 78 and a standard deviation of 6. a) What is the z-score of a student who scored 89 on the test? b) What is the z-score of a student who scored 64 on the test? c) What is the z-score of a student who scored 78 on the test? d) What is the score of a student whose z-score is 1.24? e) What is the score of a student whose z-score is -.31? f) What is the score of a student whose z-score is -1? 3. For males in a certain towWn, the systolic blood pressure is normally distributed with a mean of 135 and a standard deviation of 8. a) What is the probability that a randomly selected male's systolic blood pressure will be greater than 143? b) What is the probability that a randomly selected male's systolic blood pressure will be less than 119?9) If the sample size is multiplied by 4, what happens to the standard deviation of the distribution of sample means? A The standard error is decreased by a factor of 4. B The standard error is halved. C The standard error is doubled. D The standard error is increased by a factor of 4. It is mutiple choice10. A student from region A scored 400 on standardized math test with a mean of 350 and a standard deviation of 35. A student from region B scored 67 on a standardized math test with a mean of 62 and a standard deviation of 5. Both are being considered for a scholarship at the same university. a) How can the university decide which candidate is the better student?
- Suppose that you have a set of data that has a mean of 34 and a standard deviation of 6. a) Is the point 28 above, below, or the same as the mean. How many standard deviations is 28 from the mean. b) Is the point 46 above, below, or the same as the mean. How many standard deviations is 46 from the mean. c) Is the point 43 above, below, or the same as the mean. How many standard deviations is 43 from the mean. d) Is the point 20 above, below, or the same as the mean. How many standard deviations is 20 from the mean.1. Prove the following statements:a) The standard deviation is zero if all the observations have some constant value.b) The standard deviation does not change by the change of origin.c) The standard deviation is affected by the change of scale.9) A small value of the mean of a data set indicates that the values of that data set are spread over a relatively smaller range around the standard deviation. Select one: False True
- 6. A student got the following scores on 10 quizzes over the course of a semester: 55, 65, 70, 70, 72, 85, 90, 90, 93, 100. Calculate the a.) Range b.) MAD c.) Variance d.) Standard Deviation31 - The phones produced in factory A have a lifespan of 2900 days and a standard deviation of 100 days. The phones produced in factory B have a lifespan of 2600 days and a standard deviation of 150 days. A sample of 50 telephones was taken from factories A and B. What would be the standard error of the difference between the sample averages of the lifetimes of the phones?A) 25.49 B) 74.28 C) 29.55 D) 33.74 E) 63.96Consider two populations of students. Both populations are the same size (1000). The first population consists of all students at a grade school (grades 1-5). The second population consists of all students at a middle school (grades 6-8). Which school's population is more likely to have a larger standard deviation in the age of its students? a) The grade school's population is more likely to have the larger standard deviation. b) The middle school's population is more likely to have the larger standard deviation. c) They would most likely have the same standard deviation for age. a) It is impossible to say without more information.
- suppose the profit a Honda dealership makes on the next 5 Accords it sells are:545, 991, 902, 1,480, 1,383. Calculate the standard deviation of the sample. (please express your answer using 2 decimal places)It is reported that a survey had a standard error of the mean of 20, and it is assumed that the population standard deviation is 500. Using this information, determine the size of the sample that was used in this survey. a) 300 b) 200 c) 400 O d) 500 () e) None of the answers are correct6. Suppose that 100 females at a gym are randomly selected and asked their weights, in pounds. The mean is 137, the median is 125, and the standard deviation is approximately 23. What can you conclude? Read carefully and select one of the following: a) On average, each female's weight in the sample is approximately 23 pounds different from the mean. b) On average, each female's weight in the sample is approximately 23 pounds different from the median. c) On average, each female's weight in the sample is approximately 23% different from the mean. d) On average, each female’s weight in the sample is approximately 23% different from the median.