e1-solutions - Math 127A Exam 1 The exam has 4 problems The...

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Unformatted text preview: Math 127A Exam 1 September 22, 2010 The exam has 4 problems. The number of points is indicated. In order to receive full credit; you must provide justification for your answer. Question Points possible Points 1 20 2 40 3 80 4 60 Total 1. The department of education commissions a study into the relationship between family income and SAT scores. (a) Suggest two possible confounding factors. Explain why they are confounding. [15 points] l. Place. wl'm WM Whom (b) Is this an observational study or a controlled experiment? [5 points] Obwwkwll 3% . 2. GPAs at a certain university follow a normal curve with an average of 3.0 and a standard deviation of 0.4. There are 5500 students in the graduating class. (3.] Sketch a normal curve for GPA scores. Indicate clearly the location of the points that are 1 and 2 standard deviations from the average. [15 points] (b) In order for a student to be considered for the Dean’s list they must have a GPA of 3.6 or higher. How man}r students in the graduating class are eligible for the Dean’s list. [25 points] a: 3.5—2-0 “’ = l r * r _ __ - u: 0/0 5' ales-rt: 3’ b ’— fm___e_ “ (j 551ng 5‘ 9.1: ggybnj , loo 3. This problem is about fuel economy (measured in miles per gallon or mpg] for 1100 models of cars sold in the US in 2010. Only 10 cars had fuel economies above 40 miles per gallon. Here is the data for the remaining 1,090 vehicles. [The problem has five parts and is continued on the next page} Fuel economy Percentage Density 10— 16 12 Z F16718 12 e 18—20 16 g “9‘20722 20 10 22~ 24 14 1. lei—26 12 (a 26 7 40 14 l Left endpoints are included in the range. (a) Draw a histogram for this data, clearly indicating the scale on the vertical axis and the height of each box. [40 points] EN) | (1)) Does the data appear to follow a normal curve? Explain your answer. [10 points] l\l O i}, ‘4“ Oil 9 bi‘w. magi 91:! C, , (c) The average fuel economy is 21 mpg and the standard deviation is 6 mpg. Indicate the location of the average on your histogram and indicate the points that are within 1 standard deviation of the average. [5 points] (d) How many models of car are withing 1 standard deviation of the aVerage? [10 points] 6/9 .5\ 2 - (16" = i0?» —-(]o+i’}Dz'—?Titoif_ (e) The goveri'iment would like to impose l'uel economyr standards. As a first step they will require that all manufacturers increase fuel econom}r by 4 mpg on each model. How will this allect the average, standard deviation and shape of the histogram? [15 points] in 4. (hypothetical) The table below provides unemployment and salary information for three kinds of work- ers based on edueation level. Let’s assume that this represents the entire labor force (everyone eligible to work). Education level Number % unemployed Average salary Graduate 100 5 100,000 Bachelor’s 1000 10 70,000 High-school 10000 15 40,000 (a) What is the overall unemployment rate? [20 points] 5+ We 4 We) E l it. 8 yo (b) What is the average salary for all workers? [20 points! e' 1 0m: ro,m+{t,mxuoim 5mg WW6 (Rambo? Why/Q —. v agent i "f"; ".3 XI}? .1 MW; 3/0; GM »_ 3g) ,6 L “I; HID O (0M \WWHU 4- mm« 70 .1» fWK’wD : kt 331M 3 ll “and, M [,vC/f (e) The government wants to reduce the overall unemployment rate by 1% through job creation. How much money will they need for salaries? [20 points] W§ all may ivy, _, a} C 0"»:1} H“? llin 6ft ‘ x 3 r E” S: l 0 EV a”: “$3 (—3 .4: $2: ’_:I if“? ...
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