Probability Questions and Answers

Complete the following probability distribution table X 24 6 79 87 P X 0 23 0 3 0 18

Find Average Rate of Change from Equation Score 2 5 Penalty none Question O Watch Video Show Examples Given the function g x x 2x 9 determine the average rate of change of the function over the interval 0 6

Careers G google translate G Member Login US 4 YouTube to Mp3 C 3 CCBubble Knee Len Question 10 8 6 The function y f x is graphed below What is the average rate of change of the function f x on the interval 8 9 4 2 100 80 60 40 20 20 40 60 80 100 2 4 6 Watch Video 10 All Book Show Examples

Question Watch Video Answer Attempt 1 out of 2 Show Exam What is the intermediate step in the form x a b as a result of completing the square for the following equation 3x 9x 357 91

Question Write the expression in radical form Answer Attempt 1 out of 2 83 WIA

Question Write the expression in exponential form Answer Age 1 out of 2 F

Question Which expression is equivalent to Answer 03 8 O 3 12 34 03 20 3 16

Score 1 5 Penalty none Watch Video Answer Attempt 1 out of 2 Show Examples Question A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending The percentage of people who said the supported the plan to raise taxes was 56 The margin of error for the survey was 2 Write a confidence interval for the percentage of the population that favors the plan GEEFT

Question Answer A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate The percentage of people who said they preferred Candidate A was 28 The margin of error for the survey was 2 Which of the following is not a reasonable value for the actual percentage of the population that prefers Candidate A 26 4 O 30 8 Watch Video O 29 7 O 26 7 Show Examples Submit Answer

Question O Watch Video Statistics Calculator Show Examples The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1000 hours and a standard deviation of 20 hours What is the probability that a randomly chosen light bulb will last less than 960 hours to the nearest thousandth

Question O Watch Video Answer Attempt 1 out o Show Examples When Corey goes bowling his scores are normally distributed with a mean of 100 and a standard deviation of 10 Using the empirical rule what percentage of the games that Corey bowls does he score between 90 and 110

Question Penalty none 10 The function y f x is graphed below What is the average rate of change of the function f x on the interval 2 x 4 8 6 4 16 12 O Watch Video 10 Show Examples

Question Answer Attempt 1 out of 21 O Watch Video If using the method of completing the square to solve the quadratic equation 2 20x 33 0 which number would have to added to complete the square Submut Answer Show Examples

Question Watch Video Answer Attempt 1 out of 2 Show Examples If using the method of completing the square to solve the quadratic equation z 82 4 0 which number would have to be added to complete the square

Question Which expression is equivalent to 4 4 Answer 14 16 O 0 01

Question Solve for all values of a by factoring Answer Attempt 1 out of 2 Additional Solution No Solution P x 23x 6 2x 6 Submit Answer

8 43 of adults say cashews are their favorite kind of nut You randomly select 12 adults and ask each to name his or her favorite nut P the probability that the number who say cashews are their favorite nut is a exactly three b at least four and c at most two If convenient use technology to find the probabilities a P 3 Round to the nearest thousandth as needed b P x24 c P x 2 Round to the nearest thousandth as needed Round to the nearest thousandth as needed

7 Fifty five percent of households say they would feel secure if they had 50 000 in savings You randomly select 8 households and them if they would feel secure if they had 50 000 in savings Find the probability that the number that say they would feel secure exactly five b more than five and c at most five a Find the probability that the number that say they would feel secure is exactly five P 5 Round to three decimal places as needed b Find the probability that the number that say they would feel secure is more than five P x 5 Round to three decimal places as needed c Find the probability that the number that say they would feel secure is at most five P x5

6 32 of a certain country s voters think that it is too easy to vote in their country You randomly select 12 likely voters Find the probability that the number of likely voters who think that it easy to vote is a exactly three b at least four c less than eight a P 3 Round to three decimal places as needed b P x24 Round to three decimal places as needed c P x 8 Round to three decimal places as needed

Blood type AB is found in only 3 of the population If 290 people are chosen at random find the probability of the following the normal approximation Round your answers to four decimal places a 5 or more will have this blood type 0 8642 x b between 5 and 10 will have this blood type 0 3372 x

A fair coin is flipped 11 times Find the probability that more than 7 of the flips turn up tails O 0 100901 O 0 126692 O 0 0895181 00 113281 O 0 0609632

The owner of a small deli is trying to decide whether to discontinue selling magazines He suspects that only 9 7 of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable Before making a final decision he decides that for one day he will keep track of the number of customers that buy a magazine Assuming his suspicion that 9 7 of his customers buy a magazine is correct what is the probability that exactly 5 out of the first 10 customers buy a magazine O 0 000314609 0 00129927 O 0 000484762 0 000839050 O 0 000643632 O 0 00177055

For families with 5 children let X be the number of children with Genetic Condition B Can the following table be a probability distribution for the random variable X X P x 1 0 1594 2 0 3206 3 0 2246 4 0 1724 5 0 1231 O yes O no

Statins are used to keep cholesterol in check and are a top selling drug in the U S The equation S 1 8c 5 7 gives the amount of sales S of statin in billions of dollars a years after 1998 According to this equation how much will did people in the U S spend on statins in the year 2017 Answer People in the U S will spend billion dollars on statins in 2017

Solve 5x2 4 for a X

Solve 17 5x 8 X

Solve 9x9 5 Where x

Solve for x 52 1 31 8 11

Solve for x X 6 29

Solve for a a 8 46

The Histograms each represent part of a binomial distribution Each distribution has the same probability of success p but different numbers of trials n Identify the unusual values of x in each histog a n 4 b n 8 AP x c n 12 Q Q 0 5 0 44 0 3 0 2 0 1 0 012345678910 Q Ax 0 and x 1 B x 3 and x 4 5 AP x 0 5 0 4 0 3 0 24 0 1 0 1 012345678910 Q Q 5 OA x 0 x 1 x 2 x 3 x 4 x 5 and x 6 OB x 0 x 1 x 2 x 3 and x 4 OC x 0 and x 1 OD There are no unusual values of x in the histogram AP x Identify the unusual values of x in histogram a Choose the correct answer below 0 4 0 3 0 24 0 1 0 LAULABLA 0 1 2 3 4 5 6 7 8 9 10111213 OC x 0 x 1 x 2 x 3 and x 4 D There are no unusual values of x in the histogram Identify the unusual values of x in histogram b Choose the correct answer below OA x 0 and x 1 OB x 7 OC x 0 x 1 x 2 x 3 and x 4 OD There are no unusual values of x in the histogram Identify the unusual values of x in histogram c Choose the correct answer below

A commuter must pass through 5 traffic lights on her way to work and will have to stop at each one that is red She estimates the probability model for the number of red lights she hits as shown below Complete parts a and b X of red P X x 0 1 0 04 0 24 2 0 34 3 0 15 a How many red lights should she expect to hit each day The commuter should expect to hit 2 4 red lights each day Round to one decimal place as needed b What s the standard deviation 4 0 15 5 0 08 D The standard deviation is Round the final answer to one decimal place as needed Round all intermediate values to three decimal places as needed

It is widely accepted that people are a little taller in the morning than at night Here we perform a test on how big the difference is In a sample of 35 adults the mean difference between morning height and evening height was 5 5 millimeters mm with a standard deviation of 1 59894 mm Test the claim that on average people are more than 5 mm taller in the morning than at night Test this claim at the 0 05 significance level a Find the test statistic b Find the critical value 0 c Is there sufficient data to support the claim O Yes No

3 A popular restaurant in the mall has conducted market research on four new salads it is considering putting on the menu The percentages of study participants in various age categories and their salad preferences are shown in the table below Salad preference was found to be independent of age Salad preference Feta Cheese 10 BBQ Chicken 60 Asian Ginger 10 Chopped Cobb 20 Under 25 36 25 to 34 14 35 to 44 17 Age 45 to 54 14 55 to 64 8 65 to 74 6 75 and over 5 a People who participated in the study will be randomly selected for face to face interviews What is the probability that the marketing department will randomly select someone who is 55 or older and prefers the BBQ chicken salad b Is the event you analyzed in part a an intersection or a union How does the intersection of 55 or older and BBQ differ from the union of 55 or older and BBQ c Calculate the probability of 55 or older or BBQ using the Addition Rule How does it compare to the probability from part a 3 What is the probability that a randomly selected person from the study is under 75 years old

6 A small software company bids on two contracts It anticipates a profit of 40 000 if it gets the larger contract and a profit of 20 000 if it gets the smaller contract The company estimates that there is a 34 chance it will get the larger contract and a 62 chance it will get the smaller contract If the company does not get either contract it will neither gain nor lose money Assuming the contracts will be awarded independently what s the expected profit E X

In which of the following scenarios will conducting a paired t test for means be appropriate CHECK ALL THAT APPLY OA To test if the proportion of low income families is higher than that of high income families in British Columbia OB To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery Oc To test if there is a difference between the mean annual income of husbands and that of their wives in Canada D To test if the mean annual income of Ontarians is higher than that of British Columbians OE To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer OF To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians OG None of the above

domly selected nonfatal occupational injuries and illnesses are categorized according to the day of the week that they first occurred and the results are listed below based on data from the Bureau of Labor and Statistics Use a 0 05 significance level to test the claim that such injuries and illnesses occur with equal frequency on the different days of the week Randomly selected nonfatal occupational injuries and illnesses by the day of the week Mon Tues Wed Day Number 23 23 21 Thurs 21 Fri 19 O There is sufficient evidence to warrant rejection of the claim that injuries and illnesses occur with equal frequency on the different days of the week O There is not sufficient evidence to support the claim that injuries and illnesses occur with equal frequency on the different days of the week O There is not sufficient evidence to warrant rejection of the claim that injuries and illnesses occur with equal frequency on the different days of the week

Find the values of the slope m and the y intercept b for the line y mx b graphed below 7 6 5 7 6 54 3 The slope is m The y intercept is b 7 4 32 1 2 5 6 7 1 2 3 4 5 6 a This does not need to be written as an ordered pair

Write the equation of the line with a slope of 5 and a y intercept of 1 Y

Determine the slope and y intercept of the graph of the linear equation y 7x 1 Slope y intercept

5 G Que 4 3 2 1 S G Select an answer Quadrant I Quadrant II Quadrant III Quadrant IV x axis C Quic 5 4 E 30 2 1 1 F 2 3 4 5 For each point on the graph above select the correct location from the drop down list A Select an answer B Select an answer C Select an answer D Select an answer E Select an answer F Select an answer 1000 o forum B B 2 imp to Answer 3 4 5

Give the slope and the y intercept of the line y 62 6 Make sure the y intercept is written as a coordinate This means the y intercept must be in the form 0 b Slope y intercept

The line graph below shows the pieces of candy Sylvia ate each day of last week IU L 8 7 6 S 4 3 2 2 6 7 1 Day of Week How many pieces of candy did Sylvia eat on day 6

Give a 95 confidence interval for 2 given the following information n 45 1 2 94 81 0 7 n 50 T 2 91 82 0 55 Rounded both solutions to 2 decimal places H

In the game of roulette a player can place a 10 bet on the number 32 and have a probability 38 of winning If the metal ball lands on 32 the player gets to keep the 10 paid to play the game and the player is awarded an additional 350 Otherwise the player is awarded nothing and the casino 2023 takes the player s 10 What is the expected value of the game to the player If you played the game 1000 times how much would you expect to lose Note that the expected value is the amount on average one would expect to gain or lose each game The expected value is 0 53 Round to the nearest cent as needed The player would expect to lose about Round to the nearest cent as needed e game c al ball lan 0 Otherw

A strain of bacteria is placed into a petri dish at 30 C and allowed to grow The following data are collected Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth The population is measured using an optical device in which the amount of light that passes through the petri dish is measured Complete parts a e Time hours X 0 234 2 5 3 5 4 5 6 Population y 0 27 0 53 0 76 1 03 1 46 a Treating time x as the predictor variable use a graphing utility to fit an exponential fun the data y ab Round to four decimal places as needed

3 Use the probability distribution or histogram to find the a mean b variance c standard deviation and d expected value of the probability distribution and e interpret the results The histogram shows the distribution of household sizes in country A for a recent year a The mean is Type an integer or a decimal Do not round b The variance is Round to two decimal places as needed c The standard deviation is Round to two decimal places as needed d The expected value is Type an integer or a decimal Do not round e Interpret your results Select all that apply A Most of the household sizes differ from the expected value by 2 or 3 people B The average household is expected to have either 1 or 2 people C Most of the household sizes differ from the expected value by 1 or 2 people D The average household is expected to have either 2 or 3 people AP x 0 40 0 30 0 20 0 10 0 00 0 298 0 325 0 155 0 151 0 051 4 Household Size 0 020

A government s congress has 855 members of which 169 are women An alien lands near the congress building a treats the members of congress as as a random sample of the human race He reports to his superiors that a 95 confidence interval for the proportion of the human race that is female has a lower bound of 0 171 and an upper bound of 0 225 What is wrong with the alien s approach to estimating the proportion of the human race that is female Choose the correct answer below O A The confidence level is too high OB The sample size is more than 5 of the population size OC The sample size is too small OD The sample is not a simple random sample

Plot these points OF 6 8 7 6 54 3 2 2 21367X 8 9 56781 9 2 3 4 5 6 7 8 9 10 4

5 different color dice are rolled and the numbers showing are recorded How many different outcomes are possible Your answer is