MAT-1221 Problem Set #3 Due 13 DEC 2018 Name: Instructions: • Remember that your work is graded holistically, based on the rubric below. • Show your work. Your work should include enough detail so that one can easily understand how to work out the problem and find the answer by reading your solution. • Academic Integrity: It is okay to work together on this, and to seek help from others, so long as the problem set that you turn in accurately reflects your understanding of the problems and their solutions. Mathematics Grading Rubric 5 (100%) 4 (87%) 3 (75%) 2 (60%) 1 (40%) or 0∗ (0%) Outstanding (“A”) Good (“B”) Average (“C”) Deficient (“D”) Failing (“F”) Well-executed, well-communicated, essentially correct Generally well- Adequately exe- Flawed execution Unsatisfactory executed but may cuted but with possibly with non- execution and/or have minor com- some non-trivial er- trivial errors or poor communication munication flaws or rors or inconsistent communication with fundamental some math errors communication errors *Note: A blank page, complete nonsense or a haphazard approach (one without a reasonable direction/order) will earn a zero. MAT-1221 Problem Set #3 Due 13 DEC 2018 Formulas for Unit #3   n n! = r r!(n − r)! Pn,r = n! (n − r)! P (A ∪ B) = P (A) + P (B) − P (A ∩ B) x)2 SS(x) = x − n P X ( y)2 2 SS(y) = y − n X s2 = 2 ( P SS(x) n−1 P (A ∩ B) = P (A)P (B|A) P (A|B) = P (A ∩ B) P (B) Standard Deck of 52 Playing Cards The standard deck of playing cards which is sometimes referenced in counting and probability problems consists of 52 cards split up into four suits: diamonds (♦) and hearts (♥) which are red, and clubs (♣) and spades (♠) which are black. There are 13 cards of each suit: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. The Jack, Queen, and King are often called the “face cards”. MAT-1221 Problem Set #3 1) Refer to the Venn diagram below. How many elements are in each of the following sets? Due 13 DEC 2018 Grade: 5 b) B 0 c) A0 ∩ B d) (A ∪ B 0 )0 3 2 1 Communication strong ←− − − − − − −→ weak ×1 a) U 4 MAT-1221 Problem Set #3 Due 13 DEC 2018 2) How many 5-letter code words are possible from the first 7 letters of the alphabet (capital letters only) if a) no letters can be repeated? Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 b) if letters can be repeated? Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 c) if adjacent letters must be different? Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #3 3) From a standard 52-card deck, how many 5-card hands have 2 clubs and 3 hearts? Due 13 DEC 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #3 4) You are dealt 5 cards from a standard 52-card deck. What is the probability of being dealt a flush (all cards the same suit)? Due 13 DEC 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #3 5) What is the probability that a number selected at random from the first 600 positive integers is divisible by 6 or 9? Due 13 DEC 2018 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×2 MAT-1221 Problem Set #3 Due 13 DEC 2018 Grade: 5 4 3 2 1 6) A new lie-detector test has been devised and must Communication be tested before it is used. One hundred people are strong ←− − − − − − −→ weak selected at random, and each person draws a card ×2 from a box of 100 cards. Half the cards instruct the person to lie, and the others instruct the person to tell the truth. Of those who lied, 80% fail the new lie-detector test (that is, the test indicates lying). Of those who told the truth, 5% failed the test. What is the probability that a randomly chosen subject will have lied, given that the subject failed the test? Fill out the probability tree diagram that models this problem, and use it to help you solve. ? Told the truth Passed Test ? ? Failed Test ? ? Lied Passed Test ? Failed Test MAT-1221 Problem Set #3 Due 13 DEC 2018 7) The hemoglobin A1c test, a blood test given to diabetic patients during their periodic checkups indicates the level of control of blood sugar during the past 2 to 3 months. The following data values were obtained for 40 different diabetic patients at a university clinic: 6.5 6.4 5.0 7.9 5.0 6.0 8.0 6.0 5.6 5.6 6.5 5.6 7.6 6.0 6.1 6.0 4.8 5.7 6.4 6.2 8.0 9.2 6.6 7.7 7.5 8.1 7.2 6.7 7.9 8.0 5.9 7.7 8.0 6.5 4.0 8.2 9.2 6.6 5.7 9.0 a) Construct a grouped frequency distribution for these data, starting with the class 3.7 ≤ x < 4.7, with each class having the same width. Include a column with the class midpoints. b) Construct a frequency histogram for these data. Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 Grade: 5 4 3 2 1 Communication strong ←− − − − − − −→ weak ×1 MAT-1221 Problem Set #3 8) The frequency distribution below gives the weight loss (in pounds) for a group of patients involved in a clinical study. Compute the mean and standard deviation. Interval 0≤x
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