Normal Distributions (Ch 2) Probability (Ch 3) Permutations and Combinations Group Project 1. Suppose that your class took a test and the mean score was 70% with a standard deviation of 10%. If the test scores follow an approximately normal distribution, answer the following questions using the Empirical Rule. a. What percentage of the students had scores between 60% and 80%? b. What percentage of the students had scores between 50% and 70%? c. What percentage of the students had scores between 70% and 80%? d. What percentage of the students scored above a 90%? 2. A population has a mean of 275 and a standard deviation of 21. Find the z-score a data value of 248. Is this value unusual? Why or who not? 3a. A population has a mean of 67 and a standard deviation of 5. Find the data value that has a z-score of -1.6. b. Find the 5 number summary for this population. 4. Areal estate agent has kept records of the number of bedrooms in the houses he has sold for the last five years. The data is listed in the following table. Y ear/ Number of | one or three four five or Total Bedrooms two more 2009 2010 2011 2012 2013 Total | 2| Wn 17 28 - 54 78 133 18 258 3] L =] a. Find the probability that a randomly selected house sold by the agent had 4 bedrooms. b. Find the probability that a randomly selected house sold by the agent was sold in 2010. Find the probability that a randomly selected house sold by the agent had less than 4 bedrooms. o o . Find the probability that a randomly selected house sold by the agent was sold after 2011. 5. Suppose you roll a single fair die. What is the probability of getting a two or an even? 6. Suppose you draw one card from a standard deck of cards. What is the probability that the card is an ace or the king of diamonds? 7. In aclass of 60 students, 23 have brown hair, seven have green eyes, and three have both brown hair and green eyes. What is the probability that a randomly selected student has either brown hair or green eyes? 8. Using the real estate agent's data from problem #4 Y ear/ Number of | one or three four five or Total Bedrooms two more 2009 2010 2011 2012 2013 Total If a house is randomly selected, find: a. the probability that the house has 3 bedrooms given that it was sold in 2012. b. the probability that the house has 5 or more bedrooms and was sold in 2009. c. the probability that the house has 4 bedrooms and was sold in 2013. d. the probability that the house was sold in 2011 given that it has 4 bedrooms. 9. The new iPhone comes in 5 different colors. There are three different sizes of memory available. The store has a selection of 10 different cases to fit it. Assuming a person wants to buy an iPhone and a case, how many different phone/case combinations are possible? 10. Five friends are taking a road trip in a car that seats 5. The car has a manual transmission so only two of the friends can drive it. How many seating arrangements are possible? 11. The MAT 140 class has 15 liberal arts track students and 12 business track students. How many different combinations of subgroups of this class can be formed consisting of 3 liberal arts students and 2 business track students