Statistics Questions

Sometimes professional basketball players aren t consistent in their performance game to game Suppose that the standard deviation of the number of points scored by shooting guards in the NBA is 8 3 A random sample of 25 games played by Derrick Rose results in a sample standard deviation of 6 7 points Assume that a normal probability plot indicates that the points scored are approcimately normally distributed Is Derrick Rose more consistent than other shooting guards in the NBA at the 0 10 level of significance The null and alternative hypothesis would be Ho o 8 3 Ho 0 25 Ho o 6 7 Ho 8 3 Ho 8 3 H 0 8 3 H 0 25 H 0 6 7 H 8 3 H 8 3 The test is right tailed left tailed two tailed O Based on a sample of 25 games The test statistic is The p value is to 2 decimals to 2 decimals

20 of all college students volunteer their time Is the percentage of college students who are volunteers different for students receiving financial aid Of the 318 randomly selected students who receive financial aid 76 of them volunteered their time What can be concluded at the 0 05 level of significance Use the p value approach a For this study we should use z test for a population proportion b The null and alternative hypotheses would be Ho pv H pv c The test statistic z d The p value 0 20 0 20 please enter a decimal Please enter a decimal Please round your answer to 2 decimal places Please round your answer to 2 decimal places

The average fruit fly will lay 419 eggs into rotting fruit A biologist wants to see if the average will change for flies that have a certain gene modified The data below shows the number of eggs that were laid into rotting fruit by several fruit flies that had this gene modified Assume that the distribution of the population is normal Use the p value approach 431 410 401 437 422 405 441 422 431 449 442 441 What can be concluded at the the 0 10 level of significance level of significance a For this study we should use t test for a population mean b The null and alternative hypotheses would be Ho H

1 82 The time in minutes until the next bus departs a major bus depot follows a distribution with f x 20 where x goes from 25 to 45 minutes a Define the random variable X b X c Graph the probability distribution d The distribution is e f o name of distribution It is discrete or continuous g Find the probability that the time is at most 30 minutes Sketch and label a graph of the distribution Shade the area of interest Write the answer in a probability statement h Find the probability that the time is between 30 and 40 minutes Sketch and label a graph of the distribution Shade the area of interest Write the answer in a probability statement i P 25 x 55 State this result in a probability statement similarly to Parts g and h draw the picture and find the probability j Find the 90th percentile This means that 90 percent of the time the time is less than minutes k Find the 75th percentile In a complete sentence state what this means See Part j 1 Find the probability that the time is more than 40 minutes given or knowing that it is at least 30 minutes

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 3 15 days Is this average longer for blind dates A researcher interviewed 57 couples who had recently been on blind dates and found that they averaged 3 5 days to communicate with each other after the date was over Their standard deviation was 1 245 days What can be concluded at the the x 0 05 level of significance Use the p value approach a For this study we should use t test for a population mean b The null and alternative hypotheses would be Ho P H P

The average number of cavities that thirty year old Americans have had in their lifetimes is 5 Do twenty year olds have fewer cavities The data show the results of a survey of 13 twenty year olds who were asked how many cavities they have had Assume that the distribution of the population is normal Use the classical approach 3 6 4 6 4 4 4 6 5 6 5 6 5 What can be concluded at the a 0 05 level of significance a For this study we should use t test for a population mean b The null and alternative hypotheses would be Ho P H P

110 Researchers investigate the prevalence of a particular infectious disease in countries around the world According to their data Prevalence of this disease refers to the percentage of people ages 15 to 49 who are infected with it In South Africa the prevalence of this disease is 17 3 percent Let X the number of people you test until you find a person infected with this disease a Sketch a graph of the distribution of the discrete random variable X b What is the probability that you must test 30 people to find one with this disease c What is the probability that you must ask 10 people d Find the 1 mean and ii standard deviation of the distribution of X

Decoration Pumpkin Ghost Spiders Candy 5 2 iv not offer raisins 9 Chips 1 7 6 ii be decorated with ghosts or offer chips iii offer candy and be decorated with pumpkins Raisins 8 3 a The table above represents a record of last year s lawn decorations and Halloween treats offered at 45 houses in my neighbourhood From this information calculate the probability that a house chosen at random will i offer raisins if it is decorated with spiders 4 Time left 2 13 19 b If I roll 3 dice and select 1 card from a regular deck what is the probability that I get two 5 s or a heart

Flag question In a survey of 100 students the following table represents the number of pages of their Perception textbook students report to have completed last night Calculate mean range and standard deviation Pages 15 19 10 14 5 9 0 4 f 17 42 17 24

Simplify the following 2g 2h No Negative Exponer

In a class of 300 students Jean s standard score of 2 corresponds to a grade of 85 and Anne s standard score of 1 corresponds to a grade of 67 a What are the mean grade and the variance of the grades for the whole class

responses of 10 students who were asked how many chapters of their Perception textbook they had read and how many questions on the surprise quiz they had answered correctly Questions correct 1 3 Chapters 2 a 67 O b 82 O c 59 12 0 2 3 4 5 2 1 1 2 1 1

Simplify and solve for z 5 z 20 7 30

asked how many chapters of their Perception textbook they had read and how many questions on the surprise quiz they had answered correctly Questions correct 1 3 Chapters 2 1 0 67 O b 82 c 59 a 2 3 4 5 2 1 2 1 2 1 1

4 Which inequality represents all possible solutions of 6m n 72 B n 72 n 2 On 2

Simplify the expression com 6a76 2a b A 12a 610 B 8a b 12a f D 8a4f 0

Solve the following equation for using Fraction Busters 2 89 CT 5 355 5

Simplify the radical Give the EXACT answer in simplified radical form 8 55 20

Simplify the expression 10 4x 0y 3 12z 2y A B 325 D 3 8210 3 8 212 3y

89 The time in years after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about five years Suppose we randomly pick one retired individual We are interested in the time after age 60 to retirement a Define the random variable X b Is X continuous or discrete C X d e f Draw a graph of the probability distribution Label the axes g Find the probability that the person retired after age 70 h Do more people retire before age 65 or after age 65

Pumpkin5 Decoration Ghost 2 Spiders 9 a The table above represents a record of last year s lawn decorations and Halloween treats offered at 45 houses in my neighbourhood From this offer chips 1 7 6 information calculate the probability that a house chosen at random will 8 3 4 i offer raisins if it is decorated with spiders ii be decorated with ghosts or with pumpkins iii offer candy and be decorated iv not offer raisins b If I roll 3 dice and select 1 card from a

a Dependent on the units of measurement of the variables b An unstandardized version of the correlation coefficient A measure of the strength of the relationship between two variables Od All of the above O C

A group of researchers conducted some research in which they identified a significant correlation r 0 42 between the number of children a person has and her his life satisfaction Which of the following is inappropriate to conclude from this research All of the above are appropriate b That the directional influences of having children on life satisfaction are unclear a c 42 of variation in life satisfaction has been association with variation in the number of children d That there is a positive relationship between the number of children a person has and his her life satisfaction

Why are z scores used in Statistics a They standardize scores for a known mean and standard deviation allowing comparison O b c A z score is an outlier They allow you to allocate letters for missing values d They standardize scores in order to convert them to values closer to the mean

Flag question If a distribution has no mode what does this mean O a The data has been entered incorrectly O b It will not be a normal distribution C It will be a normal distribution O d None of the above

Flag question Is the following statement true or false The p value is independent of the sample size O True O False

Use the following information to answer the next eight exercises A distribution is given as X Exp 0 75 56 What is m 57 What is the probability density function 58 What is the cumulative distribution function 59 Draw the distribution 60 Find P x 4 61 Find the 30th percentile 62 Find the median 63 Which is larger the mean or the median

87 Suppose that the useful life of a particular car battery measured in months decays with parameter 0 025 We are interested in the life of the battery a Define the random variable X b Is X continuous or discrete C X d On average how long would you expect one car battery tollast e On average how long would you expect nine car batteries to last if they are used one after another f Find the probability that a car battery lasts more than 36 months 9 Seventy percent of the batteries last at least how long

96 At a 911 call center calls come in at an average rate of one call every two minutes Assume that the time that elapses from one call to the next has the exponential distribution a On average how much time occurs between five consecutive calls b Find the probability that after a call is received it takes more than three minutes for the next call to occur c Ninety percent of all calls occur within how many minutes of the previous call d Suppose that two minutes have elapsed since the last call Find the probability that the next call will occur within the next minute e Find the probability that fewer than 20 calls occur within an hour

82 The time in minutes until the next bus departs a major bus depot follows a distribution with f x 20 where x goes from 25 to 45 minutes a Define the random variable X b X c Graph the probability distribution d The distribution is name of distribution It is discrete or continuous e p f 0 g Find the probability that the time is at most 30 minutes Sketch and label a graph of the distribution Shade the area of interest Write the answer in a probability statement h Find the probability that the time is between 30 and 40 minutes Sketch and label a graph of the distribution Shade the area of interest Write the answer in a probability statement i P 25 x 55 State this result in a probability statement similarly to Parts g and h draw the picture and find the probability j Find the 90th percentile This means that 90 percent of the time the time is less than minutes k Find the 75th percentile In a complete sentence state what this means See Part j 1 Find the probability that the time is more than 40 minutes given or knowing that it is at least 30 minutes

Use the following information to answer the next three exercises The Sky Train from the terminal to the rental car and long term parking center is supposed to arrive every eight minutes The waiting times for the train are known to follow a uniform distribution 79 What is the average waiting time in minutes a zero b two c three d four 80 Find the 30th percentile for the waiting times in minutes a two b 2 4 c 2 75 d three

93 What is the median lifetime of these phones in years a 0 1941 b 1 3863 c 2 0794 d 5 5452

Use the following information to answer the next three exercises The average lifetime of a certain new cell phone is three years The manufacturer will replace any cell phone failing within two years of the date of purchase The lifetime of these cell phones is known to follow an exponential distribution 91 What is the decay rate a 0 3333 b 0 5000 c 2 d 3

For each probability and percentile problem draw the picture 74 Births are approximately uniformly distributed between the 52 weeks of the year They can be said to follow a uniform distribution from one to 53 spread of 52 weeks a X b Graph the probability distribution c f x d e f Find the probability that a person is born at the exact moment week 19 starts That is find P x 19 9 P 2 x 31 h Find the probability that a person is born after week 40 I P 12 xx 28 J Find the 70th percentile k Find the minimum for the upper quarter

84 A fireworks show is designed so that the time between fireworks is between one and five seconds and follows a uniform distribution a Find the average time between fireworks b Find the probability that the time between fireworks is greater than four seconds

75 A random number generator picks a number from one to nine in a uniform manner a X b Graph the probability distribution c f x d 0 0 n f P 3 5 x 7 25 g P x 5 67 h P x 5 x 3 i Find the 90th percentile

86 Suppose that the length of long distance phone calls measured in minutes is known to have an exponential distribution with the average length of a call equal to eight minutes a Define the random variable X b Is X continuous or discrete c X d e d f Draw a graph of the probability distribution Label the axes g Find the probability that a phone call lasts less than nine minutes h Find the probability that a phone call lasts more than nine minutes i Find the probability that a phone call lasts between seven and nine minutes nother on average what would you expect the total to be Why

92 What is the probability that a phone will fail within two years of the date of purchase a 0 8647 b 0 4866 c 0 2212 d 0 9997

92 A student takes a 10 question true false quiz but did not study and randomly guesses each answer Find the probability that the student passes the quiz with a grade of at least 70 percent of the questions correct

Solve each equation 72 3 2 5 6

18 Evaluate the expressions in the first column and match them with their corresponding simplified forms a 2b4c a 5f6 26 b 4a 3a 26 3 2a 6 3 DRAG DROP THE a b 3 2a a f

2 Which expression is equivalent to 21 A B D 1 1 I 27

Simplify the radical Give the exact answer in simplified radical form 27

Graph x 6 O UND

3 2 x 17 A 34 B 19 19 D 34

Solve the equation for x You can use fraction busters to help you remember the LCM HIN 56 43

26 Factory A produces 4 6 10 bolts a year and Factory B produces 6 3 10 bolts a year a What is the total number of bolts produced by these two factories b How many more bolts did Factory B produce than Factory A Total number of bolts produced Difference in the number of bolts produced DRAG DROP THE ANSWER 21 107 1 09 10 1 7 10 2 1 108 17 10 6

a b 1 Which of the following expressions are equivalent to 5 None of the above 5 4 5 5 Part B Consider the following equation 13 13 13 67 67 13 67 Here and y 1 1 1 5 5 5

Solve 3 7 11 AM 1 BV 2 6 D D x 2

Solve the following expression Select all that apply t 3 15 At 3 45 B42 C 45 D9 3