Statistics Questions

Researchers watched dolphin groups off the coast of Ireland in 1998 to determine what activities the dolphin groups partake in at certain times of the day The numbers in table below represent the number of dolphin groups that were partaking in an activity at certain times of days Activity Morning Travel Feed Social Total 6 28 38 72 Noon 6 4 5 15 Afternoon 14 0 9 23 Evening 13 56 10 79 Total 39 88 62 189 a What is the probability that a dolphin group is partaking in travel Round your final answer to 3 decimal places b What is the probability that a dolphin group is around at noon Round your final answer to 3 decimal places c What is the probability that a dolphin group is partaking in travel given that it is around at noon Round your final answer to 3 decimal places d What is the probability that a dolphin group is around at noon given that it is partaking in travel Round your final answer to 3 decimal places e What is the probability that a dolphin group is around in the afternoon given that it is partaking in travel Round your final answer to 3 decimal places

Are the events wearing a sweatshirt and failing your statistics exam independent events Why or why not OYes because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O No because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event No because they both cannot happen at the same time O Yes because they can both happen at the same time O Yes because they both cannot happen at the same time O No because they can both happen at the same time Yes because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event O No because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event

An experiment is rolling two fair dice a What is the probability that the sum is 8 Round answer to 3 decimal places b What is the probability that the sum is 8 given that the first die is a 3 Round answer to 3 decimal places c What is the probability that the first die is a 3 given that the sum is 8 Round answer to 3 decimal places d Are the events the sum is 8 and the first die is a 3 independent events Why or why not Round answer to 3 decimal places Select an answer e What is the probability that the sum is 7 Round answ to 3 decimal places f What is the probability that the sum is 7 given that the first die is a 4 Round answer to 3 decimal places g What is the probability that the first die is a 4 given that the sum is 7 Round answer to 3 decimal places

Are the events being a teenager and being in a car accident independent events Why or why not O No because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O Yes because they both cannot happen at the same time O No because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event O Yes because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event O Yes because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O No because they can both happen at the same time O No because they both cannot happen at the same time OYes because they can both happen at the same time

The number of people who survived the Titanic based on class and gender is in the following table Suppose a person is picked at random from the survivors Class 1st 2nd 3rd Total Female Male Total 135 60 195 94 24 118 79 59 138 308 143 451 a What is the probability that a survivor was female Round final answer to 3 decimal places b What is the probability that a survivor was in the 3rd class Round final answer to 3 decimal places c What is the probability that a survivor was a female given that the person was in 3rd class Round final answer to 3 decimal places I d What is the probability that a survivor was a female and in the 3rd class Round final answer to 3 decimal places e What is the probability that a survivor was a female or in the 3rd class Round final answer to 3 decimal places

Are the events clouds in the sky and raining independent events Why or why not Yes because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event No because they both cannot happen at the same time OYes because they can both happen at the same time No because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event Yes because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event No because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event O No because they can both happen at the same time Yes because they both cannot happen at the same time

Are the events passing your physics class and passing your calculus class independent events Why or why not O No because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O No because they both cannot happen at the same time O Yes because they both cannot happen at the same time Yes because the occurrence or nonoccurrence of one of them affects the probability of the occurrence of the other event O No because they can both happen at the same time O No because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event Yes because the occurrence or nonoccurrence of one of them does not affect the probability of the occurrence of the other event Yes because they can both happen at the same time

You flip a coin 5 times What is the probability that all 5 of them are tails Leave your answer as a fraction

Express the following probability as a simplified fraction and as a decimal If one person is selected from the population described in the table find the probability that the person is divorced given that this person is female Marital Status of a Certain Population Ages 18 or Older in Millions Married Divorced Widowed Total 64 66 130 Male Female Total Express the probability as a simplified fraction The probability is Type an integer or a simplified fraction Never Married 44 29 73 7 17 24 4 5 9 119 117 236

Convert the following fractions into percents and choose the appropriate result Fraction 9 100 38 40 39 50 95 U 9 78 0 W m 90 M

Solve the following using proportions Seven kg of nuts cost 5 How many kg of nuts can you buy with 2 kg

8 6 2y 3 y 4 y ne proportion for y

a Given A B C D 2 7 n 3 8 7n 3 16 Given 2n 3 56 2n 6 16 7n 21 16 b Solve the given equation Write your answer as an improper fraction in simplest n 9 7 5 2

21 Charlie bought a pair of shorts at the store when they were having a 45 off sale If the regular price of the pair of shorts was 24 how much did Charlie pay Answer

A television that normally sells for 459 is on sale at a 30 discount What is the sale price of the television 420 B 137 70 321 30 D 596 30

14 Solve for the value of z 5 SHOW HINT 25

a b Consider the two ratios 1 4 and 10 20 Are these two ratios equivalent Yes B No SHOW HINT Part B If the ratios 2 2 and 4 10 are equivalent then the value of a is

12 Use the picture to create a ratio between the objects LLLLLLLL The ratio of the number of footballs to the number of baseballs is the ratio of the number of baseballs to the number of footballs is

8 Select all that apply 40 is what percent of 25 A 160 B 1600 c625 1000 D 62 5 E 160 100 F 1600 100

If a watch costs 40 and you must pay 6 5 sales tax how much will the tax be 6 50 B 2 60 26 00 16 50

Choose the pairs of ratios below that represent equivalent rates Select all that app 1 10 20 3 B D 2 1 4 3 and and and and 6 5 16 9 20

A manufacturer wants to predict the consumer interest in a new smartphone The company uses the function below to model the number P in millions of pre orders for the phone as a function of the number d of days before the phone s release date P d 2 d 20 Number of pre orders in millions Days before the phone release date 7 How many days before the phone release will the company get 10 million pre orders Use graphing technology to find your answer Mini Lesson

Water Drain Water is draining from a tank connected to two pipes The speed f in feet per second at which water drains through the first pipe can be modeled by the function below where x is the depth of the water in the tank f x 64 x 2 Speed of water drainage in feet sec Depth of the water in the tank feel 1 What is the domain for this function Interpret the domain in context 2 Describe the end behavior for this function What does it mean for this scenario Mini Lesson

A normal distribution has a mean of 98 and a standard deviation of 6 Find the z score for a data value of 103 Round to twe

z 1 is what percentile 9 31 porcer rcentil

de The World Health Organization reports that the distribution of ages at time of death in the United States has a mean of 79 8 years and a standard deviation o of 15 5 years based on death certificates The distribution of ages at time of death is obviously left skewed thankfully few people die young and most die old Researchers plan to take a random sample of 100 American death certificates Macmillan Learning What is the probability that the mean age at time of death in a random sample of 100 American death certificates will be less than 78 years Give your answer to four decimal places P x 78

Suppose that the blood cholesterol levels of all men age 20 to 34 years follows the Normal distribution with mean H 188 milligrams per deciliter mg dl and standard deviation o 41 mg dl Macmillan Learning Choose an SRS of 1000 men from this population What is the sampling distribution of x ON 5 9451 mg dl 1 2965 mg dl ON 188 mg dl 41 mg dl ON 188 mg dl 4 1 mg dl ON 188 mg dl 1 2965 mg dl Now what is the probability that x falls within 3 mg dl of Give your answer to four decimal places P 185 191

Let s illustrate the idea of a sampling distribution in the case of a very small sample from a very small population The given population is the 10 female students in a class S t u d 0 1 2 3 4 5 6 7 8 9 e n t W ei 136 99 118 129 125 170 130 128 120 147 g ht The parameter of interest is the mean weight in pounds in this population The sample is an SRS of size n 4 drawn from the population Because the students are labeled 0 to 9 a single random digit from Table A chooses one student for the sample Macmillan Learning Find the mean of the 10 weights in the population This i the population mean Provide your answer to one decimal place

50 A department store sells sport shirts in three sizes small medium and large three patterns plaid print and stripe and two sleeve lengths long and short The accompanying tables give the proportions of shirts sold in the various category combinations Short sleeved Size S M L Long sleeved Size S M L PI PI 04 08 03 03 10 04 Pattern Pr 02 07 07 Pattern Pr 02 05 02 St St 05 12 08 03 07 08 a What is the probability that the next shirt sold is a medium long sleeved print shirt b What is the probability that the next shirt sold is a medium print shirt c What is the probability that the next shirt sold is a short sleeved shirt A long sleeved shirt d What is the probability that the size of the next shirt sold is medium That the pattern of the next shirt sold is a print e Given that the shirt just sold was a short sleeved plaid what is the probability that its size was medium Given that the shirt just sold was a medium plaid what is the probability that it was short sleeved f

In the pool example we concluded that events DF and IC are dependent events because we found that P IC DF was different from P IC O a pool can have both IC and DF a pool can have DF and not have IC OIC causes pool filters to get dirty faster

41686 6 Suppose an individual is randomly selected from the population of all adult males living in the United States Let A be the event that the selected individual is over 6 ft in height and let B be the event that the selected individ ual is a professional basketball player Which do you think is larger P A B or P B A Why

0 A friend of mine is giving a dinner party His current wine supply includes 8 bottles of zinfandel 10 of merlot and 12 of cabernet he only drinks red wine all from different wineries a If he wants to serve 3 bottles of zinfandel and serving order is important how many ways are there to do this b If 6 bottles of wine are to be randomly selected from the 30 for serving how many ways are there to do this c If 6 bottles are randomly selected how many ways are there to obtain two bottles of each variety d If 6 bottles are randomly selected what is the proba bility that this results in two bottles of each variety being chosen e If 6 bottles are randomly selected what is the proba bility that all of them are the same variety

52 A system consists of two identical pumps 1 and 2 If one pump fails the system will still operate However because of the added strain the remaining pump is now more likely to fail than was originally the case That is r P 2 fails 1 fails P 2 fails q If at least one pump fails by the end of the pump design life in 7 of all systems and both pumps fail during that period in only 1 what is the probability that pump 1 will fail during the pump design life

56 For any events A and B with P B 0 show that P A B P A B 1

Computer keyboard failures can be attributed to electri cal defects or mechanical defects A repair facility cur rently has 25 failed keyboards 6 of which have electrical defects and 19 of which have mechanical defects a How many ways are there to randomly select 5 of these keyboards for a thorough inspection without regard to order b c In how many ways can a sample of 5 keyboards be selected so that exactly two have an electrical defect If a sample of 5 keyboards is randomly selected what is the probability that at least 4 of these will have a mechanical defect

5 A sonnet is a 14 line poem in which certain rhyming patterns are followed The writer Raymond Queneau published a book containing just 10 sonnets each on a different page However these were structured such that other sonnets could be created as follows the first line of a sonnet could come from the first line on any of the 10 pages the second line could come from the second line on any of the 10 pages and so on successive lines were perforated for this purpose a How many sonnets can be created from the 10 in the book b If one of the sonnets counted in part a is selected at random what is the probability that none of its lines came from either the first or the last sonnet in the book

1 Each of a sample of four home mortgages is classified as fixed rate F or variable rate V a What are the 16 outcomes in b Which outcomes are in the event that exactly three of the selected mortgages are fixed rate c Which outcomes are in the event that all four mort gages are of the same type d Which outcomes are in the event that at most one of the four is a variable rate mortgage e What is the union of the events in parts c and d and what is the intersection of these two events f What are the union and intersection of the two events in parts b and c

16 An individual is presented with three different glasses of cola labeled C D and P He is asked to taste all three and then list them in order of preference Suppose the same cola has actually been put into all three glasses a What are the simple events in this ranking experiment and what probability would you assign to each one What is the probability that C is ranked first c What is the probability that Cis ranked first and Dis ranked last b

4 Suppose that 55 of all adults regularly consume coffee 45 regularly consume carbonated soda and 70 regu larly consume at least one of these two products a What is the probability that a randomly selected adult regularly consumes both coffee and soda b What is the probability that a randomly selected adult doesn t regularly consume at least one of these two products

Use Venn diagrams to verify the following two relationships for any events A and B these are called De Morgan s laws a AUB A B b ANB A UB Hint In each part draw a diagram corresponding to the left side and another corresponding to the right side

6 A college library has five copies of a certain text on reserve Two copies 1 and 2 are first printings and the other three 3 4 and 5 are second printings A student examines these books in random order stopping only when a second printing has been selected One possible outcome is 5 and another is 213 a List the outcomes in f b Let A denote the event that exactly one book must be examined What outcomes are in A c Let B be the event that book 5 is the one selected What outcomes are in B d Let C be the event that book I is not examined What outcomes are in C

HEAT PLAYER NAME Bam Adebayo Caleb Martin Cody Zeller Dewayne Dedmon Dru Smith Duncan Robinson Gabe Vincent Haywood Highsmith Jamal Cain Jamaree Bouyea Jimmy Butler Kevin Love Kyle Lowry Max Strus Nikola Jovic Omer Yurtseven Orlando Robinson Tyler Herro Udonis Haslem Points Per Game 20 4 9 6 6 5 5 7 2 2 6 4 9 4 4 4 5 4 3 8 22 9 7 7 11 2 11 5 5 5 4 4 3 7 20 1 3 9 107

whole NBA in 21 2022 season In other words are the players on the Miami Heat representative of the rest of the NE ms of points per game Question 1 HEAT PLAYER NAME Bam Adebayo Caleb Martin Cody Zeller Dewayne Dedmon Dru Smith Duncan Robinson Gabe Vincent Haywood Highsmith Jamal Cain Jamaree Bouyea Jimmy Butler Kevin Love Kyle Lowry Max Strus Nikola Jovic Omer Yurtseven Orlando Robinson Tyler Herro Udonis Haslem Victor Oladipo Data Points Per Game 20 4 9 6 6 5 5 7 2 2 6 4 9 4 5 4 3 8 22 9 7 7 11 2 11 5 5 5 3 7 20 1 3 9 10 7 0 pts

The quality control manager of a Taco Bell restaurant wants to analyze the length of time that a car spends at the drive through window waiting for an order It is determined that the mean time spent at the window is 61 3 seconds with a standard deviation of 13 2 seconds The distribution of time spent at the window is skewed right a What sample size is required to obtain probabilities regarding the sample mean using a normal model b The quality control manager wishes to use a new system designed to get cars through faster A random sample of 40 cars results in a mean time spent at the window of 56 8 seconds What is the probability of obtaining a sample mean of 56 8 seconds or less from the population described above Do you think the new system is effective Treat the next 55 cars that arrive as a random sample There is a 10 chance the mean time will be at or below seconds C

Scenario C David sees an ad for a new bug spray bugsBEEgone that promises to prevent bug bites better than the other leading product He decides to test this out by assigning participants into two groups one using the new bug repellent and another using a commercially available bug repellent as a control The study will measure the number of insect bites received by each participant during outdoor activities His goal is to test whether bugsBEEgone repels bugs better than his old brand What would be a Type I error for this scenario

Scenario D A researcher is interested in examining whether elementary school students social skills changed after the pandemic What is a type II error for this scenario O The researcher concludes that social skills stayed the same after the pandemic when in reality it did change O The researcher concludes that social skills did not change after the pandemic when in reality it stayed the same O The researcher concludes that social skills changed after the pandemic when in reality it did change O The researcher concludes that social skills changed after the pandemic when in reality it did not change at all

Scenario D A researcher is interested in examining whether elementary school students social skills changed after the pandemic What is a type I error for this scenario O The researcher concludes that social skills changed after the pandemic when in reality it did change O The researcher concludes that social skills changed after the pandemic when in reality it did not change at all O The researcher concludes that social skills stayed the same after the pandemic when in reality it did change O The researcher concludes that social skills did not change after the pandemic when in reality it stayed the same

Scenario D A researcher is interested in examining whether elementary school students social skills changed after the pandemic What is the alternative hypothesis for this scenario OH1 Social skills did not change after the pandemic O H1 Social skills increased after the pandemic O H1 Social skills decreased after the pandemic O H1 Social skills did change after the pandemic

Scenario D A researcher is interested in examining whether elementary school students social skills changed after the pandemic What is the null hypothesis for this scenario O Ho Social skills did not change after the pandemic O Ho Social skills increased after the pandemic O Ho Social skills did were the same or higher after the pandemic O Ho Social skills did change after the pandemic O Ho Social skills decreased after the pandemic

Scenario D A researcher is interested in examining whether elementary school students social skills changed after the pandemic Should we test this using a directional or non directional hypothesis O Directional O Non Directional