(Problem 1) A random sample of 12 customers was chosen in a supermarket. The (incomplete) results for their checkout times are shown in the table below. Checkout Time (minutes) Frequency Relative Frequency Cumulative Relative Frequency 4.0 – 5.9 2 6.0 – 7.9 0.25 8.0 – 9.9 10.0 – 11.9 1 12.0 – 13.9 2 TOTALS 12 (a – 4 points) Complete the frequency table (b – 2 points) What percent of the checkout times are at least 10 minutes? (c – 2 points) What percent of the checkout times are between 8 and 10 minutes? (d – 2 points) What percent of the checkout times are less than 12 minutes? (Problem 2) Using the data from Problem #1 … (a – 4 points) Construct a histogram (b – 2 points) In what class interval must the median lie? Assume the largest recorded checkout time was 13.2 minutes. Suppose that data point was incorrect and the actual checkout time was 13.8 minutes. (c – 2 points) Will the mean of the dataset increase decrease or remain the same and why? (d – 2 points) Will the median of the dataset increase decrease or remain the same and why? (Problem 3) A fitness center is interested in the mean amount of time the clients exercise each week. A survey will be conducted of the clients. Answer the following questions (2 points each). (a) What is the population? (b) What is the sample? (c ) What is the parameter? (d) What is the statistic ? (e) What is the variable? (Problem 4) A random sample of starting salaries for an engineer are: $38000 $42000 $44000 $48000 and $68000. Find the following and show all work (2 points each). Include equations a table or EXCEL work to show how you found your solution. (a) Mean (b) Median (c) Mode (d) Standard Deviation (e) If a recent graduate is considering a career in engineering which statistic (mean or median) should they consider when determining the starting salary they are likely to make? Explain your answer. (Problem 5) The checkout times (in minutes) for 12 randomly selected customers at a large supermarket during the store’s busiest time are as follows: 4.6 8.5 6.1 7.8 10.7 9.3 12.4 5.8 9.7 8.8 6.7 13.2 (a – 2 points) What is the mean checkout time? (b – 2 points) What is the value for the 25% percentile (first quartile) Q1? (c – 2 points) What is the value for the 50% percentile (median)? (d – 2 points) What is the value for the 75% percentile (third quartile) Q3? (e – 2 points) Construct a boxplot of the dataset. (Problem 6) Roll two fair dice. Each die has six faces. (a – 2 points) List the number of outcomes in the sample space (b – 2 points) What is the probability of rolling a 2 or a 5 on the first roll? (c – 2 points) What is the probability of rolling a 2 or 5 and then an ODD number? (d – 2 points) What is the probability the sum of the rolls is less than 4? (e – 2 points) What is the probability that the second roll is greater than 4 given that the first roll is an even number? (Problem 7) In a box of 100 cookies 36 contain chocolate and 12 contain nuts. Of those 8 cookies contain both chocolate and nuts. (a – 3 points) Draw a Venn diagram representing the sample space and label all regions (b – 1 points) What is the probability that a randomly selected cookie contains chocolate? (c – 3 points ) What is probability that a randomly selected cookie contains chocolate OR nuts? Note it cannot contain both chocolate and nuts but must have either chocolate OR nuts. (d – 3 points) What is the probability that a randomly selected cookie contains nuts given that it contains chocolate? (Problem 8)Assume a baseball team has a lineup of 9 batters. (a – 4 points) How many different batting orders are possible with these 9 players? (b – 4 points) How many different ways can I select the first 3 batters? (c – 2 points) Is a “Combination Lock” really a permutation or combination of numbers? Explain your answer. (Problem 9) You are playing a game with 3 prizes hidden behind 5 doors. One prize is worth $100 another is worth $20 and another $10. You have to pay $20 if you choose a door with no prize. (a – 4 points) Construct a probability table. See your homework for Illowsky Chapter 4 #72 and #80. (b – 3 points) What is your expected winning? (c – 3 points) What is the standard deviation of your winning? (Problem 10) Suppose that 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen. Let X be the number of students that attend graduation. As we know the distribution of X is a binomial probability distribution. Answer the following: (a – 1 point) What are the number of trials (n)? (b – 1 point) What is the probability of successes (p)? (c – 1 point) What is the probability of failures (q)? (d – 2 points) How many students are expected to attend graduation? (e – 5 points) What is the probability that 18 students attend graduation?
