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Math 10 Exam 5: Chapter 13 Name W C Each problem is worth 10 points. You must show all work to receive full credit. 1. State whether each statement is true or false. a. A normal distribution has a bell shaped curve. T b. The symbol, a, is used to indicate the standard deviation of a sample, and the symbol, s, is used to indicate the standard deviation of a population. c. A standard deviation is an average of the data. ^ d. Averages are referred to as the measures of central tendency. T e. Every 10* iPod checked for defects coming off an assembly line is an example of a stratified sample. f f In a frequency distribution, the class with the greatest frequency is called the modal class. g. The mean is found by putting the data in order and choosing the middle data value. h. The mean of a set of data will always have a z-score of 0. i. A piece of data that has a negative z-score is above the mean. j. The measures of dispersion that measures how much the data differ from the mean is called the range. \ V" 2. Choose the sampling technique that best describes each statement. i. When a sample is obtained by drawing every nth item, the sample is called a(n) C sample. ii. If a sample is drawn in such a way that each time an item is selected, each item in the population has an equal chance of being drawn, the sample is called a(n) (K^ sample. a. Random b. Cluster c. Systematic iii. When a population is divided into parts, called strata, for the purpose of drawing a sample, the procedure is known as ('\. d. Stratified iv. A sample that consists of a random selection of groups or units is called a(n) _ _ b ^ _ sample. e. Convenience V. A sample that uses data that are easily or readily obtained is called ^(n) sample. f Population 3. The cost for Florida residents to attend the University of Florida for the 2010 -2011 school year was $14,570. The circle graph below shows the percentage of that cost for tuition/fees, room, board, and computer costs. Detemine the cost, in dollars, for each category. Cost to Attend the University of Florida Computer costs = $ —-1 r for 2010-2011 Computer costs 6.2% Board 22.9% V Tuition/Fees 1 Room 36.4% Tuition/Fees = $ ^ Room - $ 2i4_s% Board = $ 4. A mean average of 80 or greater for five exams is needed for a final grade of B in a course. Say your first four exam grades are 73, 69, 85, and 80. a. What grade do you need on the fifth exam to get a B in the course? 0 b. Say your lowest grade of the exams already taken is to be dropped, what grade must you receive on your last exam to receive a B in the course? / 5. Match the distributions to each name. \. <:-.RfdctY^v\ar a. J-Shaped h. Normal I • I iv. b Morm\ 1I1 c. Rectangular It I I I d. Unbiased V. e. Skewed f. (a) (h) 6. For the set of data 23, 37, 43, 28, 43, and 45, a. Find the mean (Round to the nearest tenth if necessarj): 6P b. Find the median: ^3 ^t>(|^^9^-2> M5 ga=\Ho\ c. Find the mode: d. Find the range: G Bimodal Below is a list of survey results of daily travel times, in minutes. Create a frequency distribution table, where the first class is 25-30. 26 28 35 46 49 56 26 30 36 46 49 58 26 32 40 47 50 58 26 32 44 47 52 62 27 35 46 47 54 66 Time Traveled Frequency \ 55-60 Using the frequency table in problem #7, create a histogram of the data. 5 3 2 9. Below is a list of exam results of 13 students. Find the standard deviation of the data. 50, 60, 60, 60, 70, 70, 70, 70, 70, 80, 80, 80, 90 X dm. bo ^OCM - J ^ ^ ' \v 10. Assume the amount of time that it takes to prepare and deliver a pizza from Party Time Pizza is normally distributed with a mean of 20 minutes and a standard deviation of 5 minutes. Determine the percent of pizzas that were prepared and delivered ... a. in 16 minutes or less. 16 2JC b. in more than 26 minutes. Z^ic TO £fc c. between 18 to 23 minutes. d. Rounding to the nearest pizza, if 300 pizzas are selected at random, how many pizzas will be prepared and delivered in more than 30 minutes? ^ 30 Extra Credit (up to 10 points) Say you want to buy a house $113,500. The taxes on the house are $1200 per year, and homeowners' insurance is $320 per year. You want a conventional 10% interest rate loan requiring a 15% down payment and 3 points. Your gross income is $3990, but you have more than 10 monthly payments remaining on a car and a credit card, totaling $420. Number of Years Rale "S 10 15 4.1) $10.12451 S7.3W)S« 4S 10.36.184 7.64993 5ja 10.60655 7.90794 5.3 10.M52(,3 «. i 70S3 6.0 11.10205 »,438.'>7 6.5 I1.354W) 8.71107 7.0 11.61085 8.98828 I. 5 I1.S70IS 9,27012 8.0 12.1.1276 9.55652 S.5 12.-WS57 9.84740 <).0 12.6675X 10.14267 9.5 12.^3976 10.4-1225 10.0 13.21507 10.74605 10.5 13.49.150 I 1.05399 no 13.775(KI 11.36597 II. 5 14.05954 II.681'JO 12.0 14.34709 I2.(K>I68 2(1 a. Determine the required down payment. h. Determine the cost of the 3 points. [le m e c o s i o i m e J p o i n x s . i ^ ^ \_, c. Determine the monthly payments of the principal and interest for a 20-year loan. d. Determine the total monthly payments, including homeowners' insurance and taxes. e. Determine whether or not you qualify for the loan by being within 28% of your adjusted monthly income.