Probability Questions and Answers

Annual high temperatures in a certain location have been tracked for several years Let X represent the year and Y the high temperature Based on the data shown below calculate the correlation coefficient to three decimal places between X and Y Use your calculator r x 1 2 3 4 5 6 y 15 55 13 6 15 15 10 6 13 15 10 2

3 The probability of being dealt a full house in a hand of poker is approximately 0 0014 Find an approximation for the probability that in 1000 hands of poker you will be dealt at least 2 full houses

A manufacturer must test th bolts are too long or too sho 2 96 cm He knows that the

The board of a major credit card minutes To make sure that the randomly selected calls The me minutes is there sufficient evid confidence Step 1 of 3 State the null and

A credit score is used by credit agencies such as mortgage companies and banks to assess the creditworthiness of individuals Values range from 300 to 850 with a credit score over 700 considered to be a quality credit risk According to a survey the mean credit score is 709 1 A credit analyst wondered whether high income individuals incomes in excess of 100 000 per year had higher credit scores He obtained a random sample of 33 high income individuals and found the sample mean credit score to be 728 9 with a standard deviation of 82 5 Conduct the appropriate test to determine if high income individuals have higher credit scores at the a 0 05 level of significance State the null and alternative hypotheses Hoi H Y Tyne integers or decimals Do not round

Calcium is essential to tree growth In 1990 the concentration of calcium in precipitation in Chautauqua New York was 0 11 milligram per liter sample of 8 precipitation dates in 2018 results in the following data 0 120 0 108 0 070 0 183 0 313 0 087 0 126 0234 A normal probability plot suggests the data could come from a population that is normally distributed A boxplot does not show any outliers Does the sample evidence suggest that calcium concentrations have changed since 1990 Use the a 0 1 level of significance What are the null and alternative hypotheses Ho H Type integers or decimals Do not round mg A random

The citizens of a certain community were asked to choose their favorite pet The pie chart below shows the distribution of the citizens answers If there are 140 000 citizens in the community how many chose Fish or Cats Fish 13 Snakes 6 Hamsters 11 Cats 25 Dogs 24 Birds 21 0

Solve for the size of angle ABD Show your workings A 5cm D 6 5cm 68 B 8 4cm 50 C

parts a e Click here to view the l Distribution Area in Right Tail a If x 105 1 and s 9 8 compute the test statistic 1 Round to three decimal places as needed t Distribution Area in Right Tail dr 1 2 3 4 5 6 7 0 25 0 20 0 15 0 10 0 05 0 025 0 02 0 01 12 706 4303 6965 15 894 31 821 1 000 1 376 1 963 3 078 6 314 4 849 0 816 1061 1386 1886 2 920 0 765 0 978 1 250 1 68 2353 3 182 3 40 4 541 2 999 3 747 0 941 1190 1 533 2 132 2 776 0 741 2 757 1 156 1 476 2015 2571 0 727 0 920 2447 2 365 1 895 1860 3365 2306 0 718 0 711 0 706 0 906 0 8896 0 889 1 Distribution Arca in Right Tail 1 134 1440 1 943 1415 1 397 1 108 1 119 2612 2 517 2449 3 143 2 998 2 896 0 005 63657 9 925 5 841 4 604 4 032 3 707 3 499 3 385 1300

A 90 confidence interval for the proportion of twelfth grade students who chose mat as their favorite subject is 0 43 0 51 What was the point estimate or sample proportion used to calculate the interval

A normally distributed population has a mean of 80 and a standard deviation of 12 Refer to this information A sample of n 36 is selected What is the probability that its mean falls outside the range 79 81

Daniel wants to estimate the percentage of people who play games on their phones He surveys 350 individuals and finds that 50 play games on their phones What is the sample proportion for successes p Round the final answer to three decimal places Provide your answer below

The Indian River County Health Department needs to estimate the proportion of county residents with diabetes A health department researcher found that 161 out of a random sample of 1905 county residents had diabetes Determine the point estimate and the sample standard deviation Sp four decimal places and round the standard deviation to six decimal places if necessary p Round the sample proportion to Using a 99 confidence level determine the margin of error E and a confidence interval for the true proportion of all Indian River County residents who have diabetes Report the confidence interval using interval notation Round solutions to four decimal places if necessary The margin of error is given by E A 99 confidence interval is given by

Americans are stressed out A psychologist would like to estimate the proportion of Americans that say the future of the nation is a significant source of stress for me To help form an estimate the psychologist randomly selected 650 Americans and found that 63 of the sample agreed with the statement the future of the nation is a significant source of stress for me Using a 95 confidence level determine the margin of error E and a confidence interval for the true proportion of all Americans that say the the future of the nation is a significant source of stress for me Report the confidence interval using interval notation Round solutions to four decimal places if necessary The margin of error is given by E A 95 confidence interval is given by

An engineer has designed a valve that will mean pressure was 4 0 pounds square in mean pressure of 4 1 psi is there sufficie

The pie chart below shows how the total annual income for a certain family is spent If the amount budgeted for Insurance and Savings combined is 18 700 what is the total family income Savings 8 Insurance 9 Housing 28 Entertainment 13 Auto 13 Food 15 Clothing 14

Which of the following sets of variables could chi square be used with to identify a significant correlation Fish type plant type O Height weight Temperature rainfall Rainfall snowfall

QUESTIO The U S Energy Information A electricity this year A local po average To test their claim th 10 638 Wh of ele

The life expectancy in years of a certain type of computer chip is a continuous random variable with probability density function x c x 4 XEO 0 33 0 57 0 21 0 36 otherwise Find the probability that a randomly selected chip will last from three to seven years Round answer to two decimal places

Question 6 14 3 points Which method of data collection is used if you collect data for a study about the effects of a certain drug given to 10 patients and a placebo given to another group of 10 patients to determine if the drug is effective Perform an experiment O Use a simulation O Take a census Use sampling J A Question 7 14 2 points

The Lorenz curve for the income distribution in a certain country is given by 3 f x x x 1 Find the Gini index of income concentration II Use the answer found in 1 to determine if the income of this country is more equally distributed less equally distributed or distributed the same as a second country having an index of income concentration of 0 2 O 1 0 33 II more equally distributed 1 0 25 II more equally distributed 1 0 25 II less equally distributed 1 0 33 II less equally distributed

A recent survey reported that small small businesses in their area are n chamber conducts a survey of 87 st hours a week Assuming that the po commerce s claim at the 0 01 level

A sample of 900 computer chips revealed literature claimed that 40 fail in the firs company s claim

Wildlife conservationists studying grizzly bears in the United Standard deviation of 86 pounds Construct a 95 confide States Assume that the weights of all adult male grizzly bea

Test the hypothesis using the P value approach Be sure to verify the requirements of the test Ho p 0 52 versus H p 0 52 n 150 x 72 0 1 Is npo 1 Po 10 Yes No Use technology to find the P value P value Round to three decimal places as needed

McDonald s claims that their Monopoly game has a win rate of 25 If you play the game 300 times what is the probability that your win rate will be between 21 and 23 If there are two answers list both answers separated by a comma

The College Board reports that in 2013 the mathematics SAT scores were normally distributed with mean 451 and standard deviation 118 Students scoring in the top 5 were considered for a scholarship What math SAT score was required to be eligible for the scholarship If there are two answers list both answers separated by a comma Round your answers to nearest whole number

How I Want to Be a Teacher by Jayme I think the purpose of progressivism education is to allow our students to become engaged members of society They should know that they have a purpose in the wor and they should know how to use that role positively It is important to use class mater and make them meaningful Never leave students wondering why they have to do a assignment or read a certain book It is important to be transparent and excited abou the material we are teaching Our students reciprocate our attitudes so we need to b positive in the room I think the role of the teacher in this aspect is almost like a mentor We are preparing the students for more than college We need to prepare them for anything they can experience outside the classroom The students have an interesting role because they can decide what they learn and what they don t It really is up to them to make the most of their schooling experience 5 Which quotation best conveys the author s message A It is important to use class materials and make them meaningful B Never leave students wondering why they have to do an assignment or read a certain book I think the role of the teacher in this aspect is almost like a mentor We need to prepare them for anything they can experience outside the classroom 6 In the paragraph the word reciprocate means to A join a teacher in their understanding of the material B answer in a way that is expected by the people around you experience the same feelings for someone respond to an

You intend to estimate a population mean with the following sample 31 42 5 39 35 5 41 33 9 37 4 37 6 42 5 You believe the population is normally distributed Find the 95 confidence interval Enter your answer as an open interval This means enter your answer inside of parentheses accurate to two decimal places because the sample data are reported accurate to one decimal place For example if the lower limit is 12 2 and the upper limit is 15 3 enter your answer as 12 2 15 3 95 C I Answer should be obtained without any preliminary rounding However the critical value may be rounded to 3 decimal places Did you enter your answer as an open interval as described above

According to a survey 10 of Americans are afraid to fly Suppose 1 100 Americans are sampled a What is the probability percentage that 121 or more Americans in the survey are afraid to fly Round the percent to two decimal places b What is the probability percentage that 165 or more Americans in the survey are afraid to fly Round the percent to two decimal places c What is the probability percentage that 8 or less of the Americans surveyed answered they were afraid to fly Round the percent to two decimal places

The monthly rents in dollars paid by 8 people are given below Note that these are already ordered from least to greatest 780 865 880 890 895 990 1050 1130 Send data to calculator Suppose that one of the people moves Her rent changes from 1130 to 850 Answer the following a What happens to the median b What happens to the mean It decreases by It increases by It stays the same It decreases by 0 It increases by 0 It stays the same

Using the previous graph of f x x 6x 15x 20 estimate the intervals on which the function is concave up and concave down 40 20 4 3 2 1 20 40 y 60 Concave up 80 1 2 Concave down 3 4 5 6 7 8 An online service can give you a more accurate answer X

Mrs Jackson is a history teacher To choose two students at random she decides to choose the tallest and the shortest students in the class Mrs Jackson s strategy resulted in a fair decision

tennis player makes a dentify the distribution

Determine whether the following tables represent a probability distribution Table A Table B X 0 1 2 3 4 X 1 2 3 4 5 P x 0 674 0 280 0 044 0 003 0 001 P x 0 2 0 2 0 2 0 2 0 2 O A is a probability distribution but b is not a probability distribution ONeither A or B are probability distributions OB is aprobability distribution but A is not a probabilty distribution O Both A and B are probability distributions

For a standard normal distribution find the following Round to 3 decimal places a P Z 1 24 b P Z 0 05 c P 1 06 Z 2 28

Suppose that the heights of adult women in the United States are normally distributed with a mean of 63 5 inches and a standard deviation of 2 4 inches Salma is taller than 75 of the population of U S women How tall in inches is Salma Carry your intermediate computations to at least four decimal places Round your answer to one decimal place 11 X

Use discriminant analysis to classify the accompanying new records using only Credit Score and years Click here to view the credit approval data Click here to view the new records Records Complete the following table Round to four decimal places as needed Homeowner Credit Score Years of Credit History Revolving Balance Revolving Utilization Discriminant Score Decision Y 9 N 1 Y 6 3 12 4 N N Y 546 630 574 698 668 743 NY 21 000 4 000 8 500 16 300 2 500 16 700 546 630 574 15 90 25 70 90 18 Crean 21 000 4 000 8 500 16 300 Homeowner Credit Score Years of Credit History Revolving Balance Revolving Utilization Decision Y 9 1 6 Approve 15 90 25 70 Reject

Anita s a fast food chain specializing in hot dogs and garlic fries keeps track of the proportion of its customers who decide to eat in the restaurant as opposed to ordering the food to go so it can make decisions regarding the possible construction of in store play areas the attendance of its mascot Sammy at the franchise locations and so on Anita s reports that 45 of its customers order their food to go If this proportion is correct what is the probability that in a random sample of 4 customers at Anita s exactly 2 order their food to go Round your response to at least three decimal places If necessary consult a list of formulas

Not all visitors to a certain company s website are customers In fact the website administrator estimates that about 8 of all visitors to the website are looking for other websites Assuming that this estimate is correct find the probability that in a random sample of 4 visitors to the website exactly 2 actually are looking for the website Round your response to at least three decimal places If necessary consult a list of formulas

A logistic growth model for world population fox in billions x years after 1977 is f x According to this model the world population will be 12 billion in Round to the nearest whole number as needed 12 57 1 4 11 0 02 According to this model when will the world population be 12 billion

Statement ii and iii are true statement D E All three statements are true 4 Suppose height of individuals in a populati standard deviation of 4 inches A sample of 9 height X is computed Then p X 65 i A 0 4013 B 0 0122 O 0 7734

80 a b FIGURE P1 9 1 9 Determine angles a b and c Figure P1 9 C

1969599 page 507 M N O P C ts and Test Page

TH1507 M N O P ments and Test Pag y courses SC MATH1507 M N O P Q R S

Most users rarely tweet but the most prolific 10 create 80 of tweets from adult U S users this based on a 2019 study among a selected nationally representative sample of 2 791 U S adults who have a Twitter account and agreed to allow researchers to access that account This is O a completely randomized experiment anecdotal evidence a case control study O a voluntary sample O a matched pairs experiment O a cross sectional survey O a longitudinal cohort

Question 3 When comparing two types or condi independent random samples the comparison A versus B is made a individuals in one study for A and the B the comparison A versus B is made a

Suppose that 10 of the population of the U S is left handed If a random sample of 205 people from the U S is chosen approximate the probability that at least 17 are left handed Use the normal approximation to the binomial with a correction for continuity Round your answer to at least three decimal places Do not round any intermediate steps If necessary consult a list of formulas

The Diversity Equity and Inclusion DEI office of a major multinational bank is investigating the process used to make recent hires for financial analysts The office knows that exactly 10 of all applications were from minority candidates and that exactly 9 of the open positions were filled by members of a minority For the investigation the DEI office will take a random sample of 900 applications Let p be the proportion of minority applicants in the sample Answer the following If necessary consult a list of formulas a Find the mean of p b Find the standard deviation of p 0 c Compute an approximation for P P 0 09 which is the probability that there will be fewer minority applicants in the sample than were hired by the bank Round your answer to four decimal places 0

The records of a light bulb manufacturer show that when the manufacturing machinery is working correctly the defect rate due to imperfections in the material used is 1 The manufacturer s control department periodically tests samples of the bulbs and when 1 5 or more are defective they call repair technicians for service The control department is going to take a random sample of 4400 light bulbs Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly Answer the following If necessary consult a list of formulas a Find the mean of p 0 b Find the standard deviation of p c Compute an approximation for P 0 015 which is the probability that assuming the machinery is working correctly the repair technicians will be called Round your answer to four decimal places X