MATH 225N Week 4 Statistics Quiz Solutions.pdf, Exams of Applied Mathematics

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MATH 225N Week 4 Statistics Quiz

Solutions

Question 1

Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below. Find the boxes sold 16,14,14,21,15 - ANSWER>>> 16 Question 2 Given the frequency table below for a list of data, find the mean of the data. ValueFrequency

• ANSWER>>> 15 Question 3 Find the mode of the following list of numbers. 8,8,13,13,15,2,15,8,8,2 – ANSWER>>> 8 Question 4 The set {14,5,5,8,7,6,2,3,7,11} represents the weight in pounds for ten pigs. What is the midrange of this set? Round your answer to decimal to two places. - ANSWER>>> 3 Question 5 Given the following list of values, is the mean or the median likely to be a better measure of the center of the data set?32, 33, 36, 36, 32, 31, 32, 32, 34, 34 - ANSWER>>> Mean Question 6 Which of the data sets represented by the following box and whisker plots has the smallest standard deviation? - ANSWER>>> C

Question 7 Find the sample variance of the following set of data:4, 12, 7, 5. - ANSWER>>> 12. Q Two students, Stephanie and Maria, want to find out who has the higher GPA when compared to each of their schools. Stephanie has a GPA of 3.85, and her school has a mean GPA of 3.1 and a standard deviation of 0.4. Maria has a GPA of 3.8, and her school has a mean of 3.05 and a standard deviation of 0.2. Who has the higher GPA when compared to each of their schools? - ANSWER>>> Maria Q 9 Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. - ANSWER>>> B has larger mean. A has the larger standard deviation. Q Given the following box-and-whisker plot, decide if the data is skewed or symmetrical. - ANSWER>>> The data are skewed to the right. Q Suppose X∼N(8,1.5), and x=5. Find and interpret the z-score of the standardized normal random variable. - ANSWER>>> This means that x= is two standard deviations (2σ) below or to the left of the mean, μ=8. Q Porter's points per basketball game are normally distributed with a standard deviation of 6 points. If Porter scores 50 points, and the z-score of this value is 4, then what is his mean points in a game? Do not include the units in your answer. For example, if you found that the mean is 33 points, you would enter 33. - ANSWER>>> 26 Q In studying the relationship between average daily temperature and time spent on a telephone, suppose you computed r=0.607 using n=31 data points. Using the critical values table below, determine if the value of r is significant or not. - ANSWER>>> r is not significant because it is between the positive and negative critical values.

Q

The scatter plot below shows data relating IQ and the number of hours people spend watching TV each week. Which of the following patterns does the scatter plot show? - ANSWER>>> Negative linear pattern with deviations Q The table shows data collected on the relationship between the average daily temperature and time spent watching television. The line of best fit for the data is y^=−0.68x+85.1. According to the line of best fit, what would be the predicted number of minutes spent watching television for an average daily temperature of 32 degrees? Is it reasonable to use this line of best fit to make this prediction? - ANSWER>>> The predicted number of minutes spent watching television is 63.34, and the estimate is not reasonable. Q Find the linear regression line for the following table of values. You will need to use a calculator, spreadsheet, or statistical software. xy13.8226.0636.6246.5354.5169.36 - ANSWER>>> y=0.66x+3.

Q

A carpet store allows customers to choose carpet based on color, thread type, and thickness. If a customer can choose among 5 colors, 3 thread types, and 3 thicknesses, how many different types of carpet could the customer choose? - ANSWER>>> 45 Q Horace owns 9 science books, 12 poetry books, and 6 novels. How many total books does he own? - ANSWER>>> 27 Q Evaluate the following expression. 7!4!3! - ANSWER>>> 35 Q There are 12 candidates running for any of 6 distinct positions in a school's student council. In how many different ways could the 6 positions be filled?

• ANSWER>>> 12!/6! = 665280 Q How many distinct rearrangements of the letters in "tweedledee" are there? Give your answer as an integer. - ANSWER>>> 15120 Q A track race has 6 participants. In how many orders could the runners possibly finish? - ANSWER>>> 720 Q Victor will choose 6 colors to use for an art project. If there are 12 colors to choose from, how many different color combinations are possible? - ANSWER>>> 924 Q A car dealership offers 10 different upgrades with each of the vehicles it sells. If a customer can choose any number of upgrades offered, how many upgrade combinations are possible? - ANSWER>>> 1024 Q A particular 3rd grade class has 20 students. When the teacher checks attendance for the day, 3 are sick and 1 spends the day in the principal's

office. Assuming this is the normal occurrence for each day, what is the empirical probability that a student is not in class? Write your answer as an exact fraction which is reduced as much as possible. - ANSWER>>> 0. Q A bag of marbles contains 6 green marbles, 10 purple marbles, and 8 yellow marbles. What is the probability that a marble picked at random is green? Give your answer as a simplified fraction. - ANSWER>>> 1/ Q A pet store has the top 8 ranked dog toys. What are the chances that your dog chooses the top-ranked dog toy first and the second top-ranked dog toy second? Write your answer as an exact fraction which is reduced as much as possible. - ANSWER>>> 1/ Q An elementary school art class teacher plans to display artwork next to the door of each of the classrooms in the school. Each classroom door will only have one piece of artwork displayed, and the school has 37 such doors. If the teacher has 22 sculptures and 22 oil paintings, what is the probability that 20 sculptures and 17 oil paintings are chosen to be displayed? - ANSWER>>> (22/20)(22/17)/(44/37) Q A spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 6? Give your answer as a simplified fraction. - ANSWER>>> 21/ Q A coin is tossed 6 times. Find the probability that a heads is flipped at least once. Round your answer to two decimal places. - ANSWER>>> 0. Q A person chooses a single state from all 50 states in the United States. Find the set representing the event E that state starts with an H. - ANSWER>>> Hawaii Q A person chooses 1 odd number between 3 to 9 inclusive. What is the sample space in this experiment? - ANSWER>>> S= { 3, 4, 5, 6, 7, 8, 9} Q

If a card is picked at random from a standard 52-card deck, what is the probability of getting a black card or a Queen? - ANSWER>>> 7/ Q Suppose you took a poll of kids that like cookies. Out of 10 kids, 7 like cookies. You put each of their names in a bag and randomly draw a name, then replace the name and draw again. If you pull 3 names from the bag and replace them after each draw, what is the probability each name drawn likes cookies? Round to the nearest thousandths. - ANSWER>>> 0. Q C and D are two events with P(C)=0.4,P(D)=0.5, and P(C|D)=0.4. Calculate P(D|C). Give your answer as a decimal to the tenths place. - ANSWER>>> 0. Q A survey of households owned by couples was done. It found the number of children couples had in each household. The following probability distribution of the random variable X was created from that survey. What is the probability of more than two children in a household? X-valueP(X)-00.1310.420.3130.1140. Write your answer as a decimal. - ANSWER>>> 0. Q Let N be a random variable defined as the number of days of paid vacation for people in the U.S. Let's suppose A statistician comes up with the following probability function for N: fN(n)={0.15 for n=0,0.15 for n=5,0.35 for n=8,0.1 for n=10, and 0.25 for n=12}. What is the expected value of N? Give your answer as a decimal. - ANSWER>>> 7. Q True or False? In reference to different sampling methods, systematic sampling includes the steps: divide the population into groups; use simple random sampling to identify a proportionate number of individuals from each group. - ANSWER>>> False Q Karen wants to estimate the mean number of siblings for each student in her school. She records the number of siblings for each of 200 randomly

selected students in the school. What is the sample? - ANSWER>>> 200 randomly selected students in school. Q Select the scenario below that demonstrates sampling bias. - AWER>>> Elizabeth wants to estimate the mean height of studNSents at her school. She collects data by selecting a random group of students within her classroom. Q Karen collected data from a random sample of 1200 homeowners in her state asking whether or not they use electric heat. Based on the results, she reports that 50% of the homeowners in the nation use electric heat. Why is this statistic misleading? - ANSWER>>> The sample is biased. Q A data set is summarized in the frequency table below. Using the table, determine the number of occurrences of values greater than or equal to 6. ValueFrequency07152332435560798196104 - ANSWER>>> 20 Q Given the following histogram for a set of data, how many values in the data set are between 8.5 and 11.5? - ANSWER>>> 22 Q Find the median of the numbers in the following list. 26,13,39,22,42,39,18,21,32,14 - ANSWER>>> 24