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Download MATH 110 Module ALL MODULES (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) Exams || MATH110 Introduction and more Exams Medical statistics in PDF only on Docsity!
Mod 1 Exam 1 1.Define each of the following: a) Observation b) Element c) Variable Observation- all the information collected for each element in a study Element- in a data set, the individual and unique entry about which data has been collected, analyzed and presented in the same manner Variable- a particular, measurable attribute that the researcher believes is needed to describe the element in their study. 2.Explain outliers An outlier is a value which is out of place compared to the other values. It may be too large or too small compared ta the other values 3.Look at the following data and see if you can identify any outliers: a) Burgers, 2900(0.12)=348 b) Fish, 2900(0.28)=812 Mod 2 Exam 1. During an hour at a fast food restaurant, the following types of sandwiches are ordered: Turkey Turkey Cheeseburger Hamburger Fish Chicken Hamburger Cheeseburger Fish Hamburger Turkey Fish Chicken Chicken Fish Turkey Fish Hamburger Fish Cheeseburger Fish Cheeseburger Hamburger Fish Fish Cheeseburger Hamburger Fish Turkey Turkey Chicken Fish Chicken Cheeseburger Fish Turkey Fish Fish Hamburger Fish Fish Turkey Chicken Hamburger Fish Cheeseburger Chicken Chicken Turkey Fish Hamburger Chicken Fish a) Make a frequency distribution for this data. 430 389 414 401 466 421 399 387 450 407 392 410 440 417 471 Find the 40th percentile of this data. There are a total of fifteen numbers, so n= 15. In order to find the percentiles, we must put the numbers in ascending order: 387 389 392 399 401 407 410 414417 421 430 440 450 466 471 For the 40th percentile: 40 i=(5)n= (Fo) 15 = 6 Therefore, the 40th percentile index for this data set is the 6th observation. In the list above, the 6th observation is 407. 3. Consider the following data: (29, 20, 24, 18, 32, 21} a) Find the sample mean of this data. b) Find the range of this data. c) Find the sample standard deviation of this data. d) Find the coefficient of variation. b) The range is the largest value minus the smallest value: Range = 32 - 18= 14 There are six points, so n=6. {29, 20, 24, 18, 32,21} a) The sample mean is given by: Lay _ 29+20+ 24+ 18+ 32+ 21 " aT z= 7 c) In order to find the sample standard deviation, we must first find the sample variance: 4g? = LGUT EP _ (29-24)? + (20-24)? + (24 ~ 24)? + (4B ~ 24)? + (32 24)? + (21-24)? _ at an 6-4 = The standard deviation is given by: s=/s? = /30=5.478 d) Is the point 79 above, below, or the same as the mean. How many standard deviations is 79 from the mean. a) The data point 57 is above the mean. Now use the z-score to determine how many standard deviations 57 is above the mean. We are told that the mean is 49 and the standard deviation is 8. So, the z-score is given by: The z-score is 1, so the data point 57 is 1 standard deviation above the mean. b) The data point 33 is below the mean. Now use the z-score to determine how many standard deviations 33 is below the mean. We are told that the mean is 49 and the standard deviation is 8. So, the z-score is given by: The z-score is -2, so the data point 33 is 2 standard deviations below the mean (the negative sign indicates that the point is below the mean). c) The data point 31 is below the mean. Now use the z-score to determine how many standard deviations 31 is below the mean. We are told that the mean is 49 and the standard deviation is 8. So, the z-score is given by: {20, 5, 12, 29, 18, 21, 10, 15} a) Find the median. b) Find the mode of this set. a) In order to find the median, we must first put the numbers in ascending order: 5, 10, 12, 15, 18, 20, 21, 29. Notice that there are two “middle” numbers, 15 and 18. The median is the average of these two numbers. Median = (15+18)/2 = 16.5. b) No number occurs more than once, so there is “no mode”. Exam 3 1. Find the answer to each of the following by first reducing the fractions as much as possible: a) P(412,3)= b) C(587,585)= n! "inv! nt (rr)! P(n,r)= Clan) —|_ 412! 412! 412-411-410 a. P(412,3)=| Ga-9 ~ o C 69, 426, 120 b.C(587,585)=| sarees = Fag = er = 171,991 2. Suppose you are going to make a password that consists of 5 characters chosen from {1,2,4,9,d,i,.k,m,n,w,z}. How many w P(B)=1-.45=.55. 4. Suppose A and B are two events with probabilities: P(A‘ )=.50, P(B)=.65, P(ANB)=.30. a) What is (A | B) ? ») What is (B | A) ? a. For P(4|8) use P(a|B) ="2) PAB) = 2 = 4615 b. P(ANB) P(A) For P(B|4) use P(BJA) = P(BIA) = = = .60. 5. In a manufacturing plant, three machines A, B, and C produce 30 %, 20 %, and 50 %, respectively, of the total parts production. The company's quality control department determined that 3 % of the parts produced by machine A, 2.5 % of the parts produced by machine B, and 4 % of the parts produced by machine C are defective. If a part is selected at random and found to be defective, what is the probability that it was produced by machine B? 
