Math 115 Fall 2023 Final Exam Practice Problems Overview

Math 115 Fall 2023 Final exam practice problems 1) The Eatonville Zoo has both the world's tallest and shortest penguins, Emperor penguins which are the world's tallest penguins and Little Blue ( Fairy ) penguins which are the world's shortest penguins . Below is a sample of the heights , in feet , of 10 randomly selected full- grown Emperor penguins at the zoo . Find the indicated statistics for these penguin heights . You may use the calculator shortcut to receive full credit. {3.2 , 3.6 , 4.1 , 4.7 , 3.8 , 2.9 , 4.3 , 3.2 , 3.1 , 3.3} 1A) X = 1B) S = 1c) S2 = = 1D) What is the sample frequency of full- grown Emperor penguins that are over 4.0 feet tall ? 1E) What is the sample proportion of full- grown Emperor penguins that are under 4.0 feet tall ? 2) Full- grown Emperor penguin heights are normally distributed ( symmetric ) with an average height of 3.6 feet with a standard deviation of 0.5 feet . Fill in the blanks below according to the Empirical Rule . Hint : how many standard deviations away from the mean are those numbers ? % of the penguins are between 3.1 and 4.1 feet tall . % of the penguins are between 2.6 and 4.6 feet tall .

% of the penguins are between 2.1 and 5.1 feet tall . 3 ) The table below has information about the coins in Lulu's collection . Penny Nickel Dime Quarter TOTALS Earned 14 23 92 77 206 Given 11 32 158 93 294 TOTALS 25 55 250 170 500 Show all work including your fractions , you do not need to simplify them . An answer 3 5 8 56 such as is perfectly acceptable . 3A) If ONE coin is randomly selected , what is the probability that it is a coin that Lulu earned ? 3B) If ONE coin is randomly selected , what is the probability it is a dime and it is a coin that was given to Lulu ? 3C) If ONE coin is randomly selected, what is the probability it is a quarter given it is a coin that Lulu earned ?

3D) If ONE coin is randomly selected , what is the probability that it is a penny or it is a coin that was given to Lulu? 3E) If TWO coins are randomly selected with replacement, what is the probability that they are both nickels ? 3F) If THREE different coins are randomly selected without replacement , what is the probability that the first is a quarter , the second is a dime and the third is a penny ? ( Notice you are not allowed to choose the same coin more than once ) 4 ) Recall that Lulu's coin collection has a mean cash value of μ = 14.1 cents and a standard deviation of σ = 8.15 cents. Penny Nickel Dime Quarter Value in cents 1 5 10 25 Probability 0.05 0.11 0.50 0.34 4A) Use the definition of the mean of a discrete population μ = ΣxP( x ) to show that the average cash value of her coins is 14.1 cents . 2

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4B) Use the definition of the mean of a discrete population ơ =Σ( x - μ)2 P (x) to show that the standard deviation of the cash value of her coins is 8.15 cents. 4C ) Fill in the blanks below according to the Empirical Rule . % of the coins fall within 8.15 cents of the 14.1 cents. % of the coins fall within 16.3 cents of the 14.1 cents % of the coins fall within 24.45 cents of the 14.1 cents. 5 ) Partial credit will be given if you only use the calculator shortcut to find the values and show no work . For full credit you must show all of the work . Write down the formula (s) you are using and then all of the calculations you do to find the final answers . Use the appropriate symbols for each statistic. For the following for the data set { 12 , 20 , 7 } find : 5A) Mean 5B) Variance 5C) Standard deviation 6) (20 points) The three most popular table games at the Casino International are blackjack , craps and Let it Ride . The table below indicates the number of people who are playing at this moment and the minimum bet allowed at the table they are playing on. Blackjack Craps Let it Ride TOTALS

$ 10 minimum 101 40 28 169 $ 50 minimum 30 11 7 48 TOTALS 131 51 35 217 Show all work including your fractions , you do not need to simplify them . An answer 3 5 8 56 such as is perfectly acceptable . 6A) If ONE player is randomly selected , what is the probability that they are playing blackjack ? 6B ) If ONE player is randomly selected , what is the probability that they are playing Let it Ride at a table with a $ 10 minimum ? 6C ) If ONE player is randomly selected , what is the probability that they are at a table with a $ 50 minimum given they are playing blackjack ? 6D) If ONE player is randomly selected , what is the probability that they are playing craps or they are at a table with a $ 50 minimum?

6E ) If THREE different players are randomly selected , what is the probability that they are all at tables with a $ 10 minimum ? ( Notice you are not allowed to choose the same player twice ) 7) When playing Craps , the "shooter " rolls two fair six - sided dice and the sum of the two dice added together is what matters most . It turns out that the sum of the two dice are symmetrically distributed with u = 7 and σ = 210 36 ( ≈ 2.42) . 7A ) According to the Empirical Rule, the percentage of times that the sum of the two dice is within 3 standard deviations of the mean of 7 is approximately equal to % . 7B ) According to the Empirical Rule, the percentage of times that the sum of the two dice is within 2 standard deviations of the mean of 7 is approximately equal to % . 8 ) You and 29 of your closest friends are on spring break and you find yourself standing at the door of the Casino International where you are greeted by the owner, Fez . " Welcome to my country , " you hear him say with a heavy but non-specific adorable forcign acccnt . Fcz is standing next to a giant slot machine and offers to give you a frec spin to entice you into the Casino International . The table below lists the possible outcomes for a spin on the slot machine along with their corresponding probabilities. $ P($) 0 0.68 3 0.31 12 0.01

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Calculate the value of the mean and standard deviation of the slot machine outcomes. Partial credit will be given if you only use the calculator shortcut to find the values and show no work . For full credit you must show all of the work . Write down the formula ( s ) you are using and then all of the calculations you do to find the final answers . Use the appropriate symbols for each parameter. 9) In the game of roulette , there is a wheel with 38 different numbers on it. The wheel is spun and a ball circulates around the edge of the wheel until the ball falls into one of the numbered slots on the wheel . The numbers are 0 , 00 , 1 , 2 , 3 , ... , up to 36. For betting purposes , the two numbers 0 and 00 are not considered to be odd numbers or even numbers , therefore there are 18 odd numbers and 18 even numbers on the wheel . Show all work including your fractions , you do not need to simplify them . An answer 3 is perfectly acceptable . such as 8 56 For the first spin of the wheel you decide to bet on the number 7. For the second spin you bet on " even " meaning if the ball lands on any even number you win. 9A ) What is the probability that you will win your bet on 7 ? 9B) What is the probability that you will win your bet on even ? 9C) What is the probability that you will win both bets ? 9D) What is the probability that you win your bet on 7 or you win your bet on even ? 10) SHOW ALL OF YOUR WORK. ( Don't just use the calculator shortcut . ) Find the following for the data set {3 , 5, 13).

10A) Mean 10B) Variance 11) Short answer questions. 11A ) You are doing a left tailed test with the test statistic : x2 = 15.4 . Find the p - value for this hypothesis test . 11B) You are doing a two - tailed test with the test statistic is : t = −1.54 . Find the p-value for this hypothesis test . 11C) You are testing H1 : σ > 100 with S = 114 and the p - value = 0.037 . What is " more convincing data ” in this situation ?

11D) Write the correct conclusion to thc tcst in part C above using statistical languagc and in “ plain English" / non-technical terms . ( Use a = 0.05) 12) Multiple choice questions , write the number of your answer on the provided blank line. A) Which of these tells you the average distance from the mean ? 1) Median 2) Sample proportion 3) Average 4 ) Standard deviation 5) Variance Σχ Σ( x - x ) 2 2 B) n - 1 Is the formula for calculating which sample statistic ? 1) Variance 2 ) Median 3) Mean 4) Standard Deviation 5) Midrange C ) Which of these is a correct statement about the terms parameter and statistic ? 1 ) σ is a parameter and a statistic . 2) A parameter is a measurement of a population a statistic is a measurement of a sample . 3) A statistic is a measurement of a population a parameter is a measurement of a sample. 4 ) X is a parameter , but μ is a statistic . 5) A parameter is the opposite of a statistic .

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D) What is the mean of the Z distribution ? 1) 0 2) 1 3) The degrees of freedom 4) 2 times the degrees of freedom 5 ) a + b 2 E) You are sampling from a Chi - squared distribution with 34 degrees of freedom and your sample has 93 values . Which of these is true about the distribution of X ? 1) It is also a Chi - squared distribution 2) It is approximately uniformly distributed 3) It is normally distributed 4 ) It is approximately normally distributed 5 ) It is not normally distributed nor is it approximately normal . F) You are doing a hypothesis test with H1 : P0.5. Which of these sample values would be the most convincing evidence that H1 is true ? 1 ) P =0.4 2) P= 0.5 3) P = 0.6 4) P= 0.7 5) P = 0.8 G ) You are doing a hypothesis test with H1 : μ > 50, X = 63, S = 23 , n = 17 and the population is bi - modal . Which of these test statistics should you use? σ X - μ 1) T = =

- Z χ - μ 2) T = Z 3) Neither , because the population is not normal. S √ n √ n 4 ) Neither , because the sample size is less than 30 . 5) Neither because the population is not normal, and the sample size is less than 30 . H ) Which of these test statistic formulas requires that the population you are sampling from be normally distributed ? 1) T = χ -μ σ √ n = (n - 1 ) s2 4) T = σ 2 Z 2) T =· χ -μ S p - p n - 1 3) T = p ( 1 - p ) n 2 n - 1 √

n 5) T = [(0- E) 2 = x2 Σ E 2 I) If you are testing II1 : μ > 20 which of these would you need to see in your sample to convince you that H1 is true ? 1) p =67 2) S = 67 3) X = 67 4) μ = 67 J) Which of these cannot be an alternative hypothesis ? 1) μ ± 56 2) p =0.56 3) σ > 56 4) μ < 56 K) If the p- value is more than a then you should 1) Support the NULL hypothesis 2 ) Fail to reject the NULL hypothesis 3) Reject the NULL hypothesis 4 ) None of the above

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For all problems from here on assume that all requirements have been met to complete the hypothesis test or find the confidence intervals . In my opinion , Mount Rainier in Washington State is the most majestic mountain in America. It rises from sea level to a peak height of 14,410 feet . That is more than double the height of Mount Mitchel , NC , the highest point in the United States east of the Mississippi River ! Mount Rainier is so massive that the Wonderland Trail that encircles it at an average elevation of nearly a mile above sea level is 93 miles long. 13) The number of miles hiked per day by hikers on the Wonderland Trail are normally distributed with an average of 10.2 miles per day and a standard deviation of 3.3 miles per day . Answer the following questions , showing all the work . 13A) What is the probability that a random hiker covers less than 8 miles in a day ? 13B) How many miles does a random hiker have to hike on a random day to say , " Only 7 % of hikers ever hike more miles on this trail than I did today ” ? 13C) What is the probability that for a sample of 21 randomly selected hikers the average number of miles hiked per day is more than 12 miles? 14 ) The Iditarod dog sled race runs annually from Anchorage to Nome , Alaska . The course alternates yearly between a northern and southern route , which after adjustments based on current trail conditions is usually about 1,000 miles long . A random selection of 308 Iditarod finishers from various years found that 71 were female .

14A) Can you conclude that more than 18 % of all Iditarod finishers are female ? a = 0.01 14B ) Find a 95 % confidence interval for the percentage of Iditarod finishers that are female. 14C) Find a 90 % confidence interval for the percentage of Iditarod finishers that are female. 14D) What impact did changing the confidence level from 95 % to 90 % have on the resulting confidence interval ? 15) The world - famous bakery , The C & C Munchie Factory , specializes in cookies and cupcakes that are so delicious they make everybody dance now . One of the quirky things about the bakery is that they sell their cupcakes

by the pound . Assume the number of pounds of cupcakes sold per day is normally distributed with a mean of 212 pounds and a standard deviation of 43 pounds . 15A) How many pounds of cupcakes do they sell on their best 1 % of sales days ? 15B ) For a randomly selected day , what is the probability that they sell between 200 and 220 pounds of cupcakes ? 15C) If five days are randomly selected , what is the probability that they sell between 200 and 220 pounds of cupcakes on each of the 5 days ? 15D ) If five days are randomly selected , what is the probability that the average number of pounds of cupcakes they sell is between 200 pounds and 220 pounds ? 16 ) As you know , the world - famous bakery The C& C Munchie Factory , specializes in cookies and cupcakes that are so delicious they make everybody dance now . Each customer chooses a cupcake without icing on it and the flavor of icing that they want . The server starts putting a swirl of icing on the cupcake and keeps going until the customer says " stop " . One of the quirky things about the bakery is that they sell their cupcakes by the pound ! For these problems we are only interested in cupcakes with icing on them. You have been given information about a random sample of 1200 iced cupcakes the bakery sold . You know how many of each cake type were sold and how many with each type of icing were sold .

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However , you do not know how many of each combination they sold . For all you know all of the 137 cupcakes with peanut butter icing were made of Lemon cake . You also know that for this sample of 1200 cupcakes , the average weight is 0.72 pounds , and the standard deviation is 0.32 pounds. Assume that the weights of the cupcakes are normally distributed. Sponge Chocolate Red Velvet Lemon Total Butter Cream ? ? ? ? 252 Vanilla Bean ? ? ? ? 232 Chocolate Fudge ? ? ? ? 306 Peanut Butter ? ? ? ? 137 Strawberry ? ? ? ? 55 Maple & Bacon ? ? ? ? 157 Key Lime ? ? ? ? 61 Total 370

426 231 173 1200 For this sample of 1200 cupcakes, the average weight is 0.72 pounds, and the standard deviation is 0.32 pounds. Assume that the weights of the cupcakes are normally distributed. 16A) Do less than 40 % of the cupcakes that they sell have chocolatc cakc ? Usc a 0.01 significance level . 16B ) According to The C & C Munchie Factory website , the average cupcake weighs more than 11 ounces ( 0.6875 pounds ) Use a = 0.05 . Does this sample confirm the website's statement ? 16C) The C & C Munchie Factory website also says the standard deviation of their iced cupcakes is 1/3 of a pound. a = 0.05 Does this sample contradict this statement ? 17 ) One of the many natural wonders to be seen in the San Juan islands is the annual migration of Orca whales. The number of Orca whales in a pod are approximately normally distributed , with a mean of 22.4 whales and a standard deviation of 3.8 whales .

17A ) What is the probability that the average number of Orca whales in a sample of 34 randomly selected pods is less than 20 ? 17B ) How many Orcas are in the 10 % of pods that have the fewest members ? 17C) What is the probability that a random Orca whale pod has more than 28 whales ? 18) A study of 375 daily calorie consumption totals for dogs competing in the Iditarod found that the dogs in the study averaged 10,065 calories per day with a standard deviation of 830 calories . Assume that calories per day are normally distributed. 18A) Can the researchers conclude that the standard deviation in the number of calories consumed per day by dogs competing in the Iditarod is less than 1,000 calories ? Let α = 0.05

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18B) Can the researchers conclude that the average number of calories consumed per day by dogs competing in the Iditarod is 10,000 calories ? Let a = 0.05 18) (Continued) A study of 375 daily calorie consumption totals for dogs competing in the Iditarod found that the dogs in the study averaged 10,065 calories per day with a standard deviation of 830 calories . Assume that calories per day are normally distributed . 18C ) Find a 90 % confidence interval for the mean number of calories consumed per day by dogs competing in the Iditarod . 18D ) Now assume the study instead only had 37 dogs and find a 90 % confidence interval for the mean number of calories consumed per day by dogs competing in the Iditarod. 18E ) What impact did changing the sample size from 375 to 37 have on the resulting confidence interval ? 18F ) Find a 95 % confidence interval for the variance in the number of calories consumed per day by dogs competing in the Iditarod . Keep using n = 37 . 18G ) Find a 98 % confidence interval for the standard deviation in the number of calories consumed

per day by dogs competing in the Iditarod . Keep using n = 37 .

2023 Fall Math 115 Final Exam Practice Problems for print

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