Answers Only VI- Counting Principles; Further Probability Topics

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1 Answers Only VI- Counting Principles; Further Probability Topics 1) If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability that all 3 cards are clubs. (Type a fraction. Simplify your answer) = s = = ) A grab bag contains 12 $1 prizes, 6 $5 prizes, and 3 $20 prizes. Three prizes are chosen at random. Find the following probabilities. a. The probability that exactly two $20 prizes are chosen is (Round to the nearest thousandth as needed) = 3 = = b. (have to answer a to get the rest)??? 3) A die is rolled 10 times. Find the probability of rolling exactly 1 five. (Type an integer or decimal rounded to four decimal places as needed) 10! 1 1 (10 1!)(1!) = ) The probability of rolling no more than 4 twos is (Type an integer or decimal rounded to four decimal places as needed. Round all intermediate values to four decimal places as needed.)

2 5) When treated with an antibiotic, 94% of all the dolphins are cured of an ear infection. If 7 dolphins are treated, find the probability that exactly 3 are cured. (Round your answer to 4 decimal places) 7! (4!)(3!) (0.94)3 (0.06) V- Sets and Probability 6) A survey of magazine subscribers placed 65 celebrities in 3 categories. 40 were on the most powerful list. 32 were on the most liked list. 24 were on the most intelligent list. 4 were on all three lists. 18 were on the most powerful and most liked lists. 14 were on the most powerful and most intelligent lists. 9 were on the most liked and most intelligent lists. How many were only on the most powerful list? There were 12 celebrities that were only on the most powerful list. However the totals don t add up to 65! I calculate that 6 must be on no list at all. 7) Suppose 22% of the population are 62 or over, 28% of those 62 or over have loans, and 53% of those under 62 have loans. Find the probabilities that a person fits into the following categories. a. 62 or over and has a loan (Type an integer or decimal rounded to three decimal places as needed) = b. Has a loan ( ) + ( ) = I - Liner Functions 8) Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b. (4,6); x+2y=5 (Simplify your answer. Use integers or fraction for any numbers in the expression.) y = 1 2 x = 1 2 (4) + b b = 8 y = 1 2 x + 8

3 Random Variable 9) Find the expected value of the random variable. Table: X/P(x) 2/0.1 3/0.4 4/0.1 5/0.4 What is the expected value? 2(0.1) + 3(0.4) + 4(0.1) + 5(0.4) = = 3.8 Standard Deviations 10) Find the percentage of area under a normal curve between the mean and the given number of standard deviations from the mean. This problem can be solved using technology or the table for the standard normal curve from your text. 0.4 % (Round to the nearest integer as needed) N(0.4) N(0) = % 11) Find the z- score that best satisfies the condition. This problem can be solved using technology or the table for the standard normal curve from your text. 14% of the total area is to the left of z z= (Round to the nearest hundredth as needed) z = ) Suppose 16 coins are tossed. Find the probability of getting the following result using the binomial probability formula and the normal curve approximation. Exactly 12 heads Use the table of areas under the standard normal curve given below. Binomial probability= (Round to 4 decimal places) 16! 1 12 (12!)(4!) = = =

4 Second Set 1) Find the standard deviation for the set of numbers. 19,17,19,9,10,20,11,6,13 a. 5.5 b. 1.7 c. 4.8 d ) Find the percent of the total area under the standard normal curve between the given z- scores. Z= and z= 0.0 a b c d ) Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent. The average weekly income of teaches in one school district is $390 with a standard deviation of $45. What is the probability of a teacher earning more than $425 a week? (Show work) P = 1 N % 45 4) Find the mode or modes. 20,31,46,31,49,31,49 a b. 49 c. 31 d. No mode 5)Skip

5 6) Use the normal curve approximation to the binomial distribution. Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective. (Show work) Result using Binomial distribution: ! P(k 219) = 1 k!(10000 k)! (0.02)k (0.98) k = % k =0 Approximate result using normal distrubution, µ = np = 10000(0.02) = 200 σ = np(1 p) = 10000(0.02)(0.98) z = (0.02)(0.98) = P(x z) = % 7) Find the median for the list of numbers. 6, 7, 20, 29, 43, 43, 45 a. 20 b. 29 c. 28 d. 43 8) Find the range for the set of numbers. 5, 18, 3, 15, 9 a. 15 b. 18 c. 3 d. 4 9) Find a z- score satisfying the given condition. 30.2% of the total area is to the right of the z. a b c d

6 10) Assume the distribution is normal. Use the area of the normal cure to answer the question. Round to the nearest whole percent. The mean clotting time of blood is 7.35 seconds, with a standard deviation of 0.35 second. What is the probability that blood clotting time will be less than 7.0 seconds? a. 16% b. 15% c. 84% d. 14% 11) Find a z- score satisfying the given condition. 4% of the total area is to the left of z. a b c d ) To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below. Find the standard deviation. Round to the nearest ten cents. $ 263 $271 $243 $292 $248 $118 $113 $207 (Show answer) ( ) x = = s 2 = 1 (x 7 i x ) 2 = i=1 s = $ Find the range for the set of numbers. 73, 144, 33, 116, 199 a. 71 b. 166 c. 199 d. 33

7 14) Find the mean. Round to the nearest tenth. Value/Frequency 12/3 19/5 23/3 27/6 34/1 37/1 (Show work) 12(3) +19(5) + 23(3) + 27(6) + 34(1) + 37(1) = ) Find the mean for the list of numbers. 45,47,94,57,124,68 (Round to the nearest tenth) a. 72 b. 73 c. 73 d. 87 m = 72.5 (Above choices are not correct to the nearest tenth. Furthermore, b and c are identical!) 16) Use the normal curve approximation to the binomial distribution. A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct. a b c d µ = np = = 15 σ = np(1 p) = = % of 60 = z = = P(x > z) =

8 17) Find the percent of the area under a normal curve between the mean and the given number of standard deviations from the mean a % b % c % d % 18) Find the mean for the list of numbers. 17, 4, 29, 17 (Round to the nearest tenth, if necessary) a b c d ) Find the mode or modes. 92, 50, 32, 50, 29, 92 a. 92, 50 b. 92 c d. No Mode 20) A die is rolled five times. Find the probability of getting the indicated result. Two comes up one time. a b c d ! 1 P(k = 1) = 1 (4!)(1!) = =

9 21) In a certain distribution of numbers, the mean is 50 with a standard deviation of 6. Use the Chebyshev s theorem to tell the probability that a number lies in the indicated interval. Between 26 and 74 a. At least 1/16 b. At least 8/9 C. At least 15/16 d. At least 24/25 No more than k 2 of the data can be beyond kσ of the mean: P( x > kσ ) 1 k 2 k = 24 6 = 4 ( ) = 1 P x > kσ P kσ < x < kσ ( ) = ) Find the mean. Round to the nearest tenth. Value/ Frequency 12/1 17/5 24/4 31/2 32/2 a b d (1) +17(5) + 24(4) + 31(2) + 32(2) = (Answer not in above choices.) 23) Find the median for the list of numbers. 10, 10, 22, 13, 23, 47, 37, 32 a b c. 23 d. 22

10 24) Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of the indicated result. Exactly 275 heads a b c d σ = 125 = 5 5 = N x < 26 N x < 24 = σ σ