Probability Questions and Answers

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 2332 2 0 0311 3 0 114 4 0 5199 0 1018 LO 5 O no Q yes

Complete the following probability distribution table X 27 12 49 67 86 P X 0 24 0 14 0 26 0 2

Can the following table be a probability distribution X P x 1 0 2077 2 0 0943 3 0 3281 4 0 1105 5 0 3232 O yes O no

Write 3 078 102 in standard notation

Translate the following verbal statement into an algebraic equation and then solve Use for your variable The sum of three times a number and six is nine Equation x

x 6 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 Clear All Draw

You want to obtain a sample to estimate a population proportion Based on previous evidence you believe the population proportion is approximately p 0 29 You would like to be 98 confident that your esimate is within 1 5 of the true population proportion How large of a sample size is required n

dy dt y 6t y 0 5 In this question we will use a spreadsheet to approximate the value y 1 The picture below shows a spreadsheet being used to implement a linear approximation scheme ie Euler s method with initial value y0 y 0 5 and a step size of 0 1 to make such an approximation in 10 steps A downwards arrow indicates that the contents from the cell above will be dragged down Column B holds values of t Column A holds approximations of y t and Column C holds approximations of y t a Which entry should go in cell C1 A B1 0 1 B B1 1 C A1 5 B1 D A1 0 1 6 B1 E A1 B1 F A1 6 B1 c Which entry should go in cell B2 A 0 B 1 C B1 0 1 D A1 6 C1 E A1 6 B1 F C1 0 1 b Which entry should go in cell A2 A A1 0 1 B A1 0 1 B1 C 0 1 D B1 0 1 C1 E A1 0 1 C1 F A1 6 B1 1 2 3 4 5 67892 10 A 5 B 0 C

Question Draw Graph Reset O Watch Video The function f x log x 3 4 is graphed below Plot all lattice points of the inverse Use the labeled points as your guide Click on the graph to plot a point Click a point to delete it Show Examples

Question What are the features of the function f x 3 1 graphed below Answer Attempt 1 out of 2 The function f x is and it is Submit Answer 12 11 10 9 8 7 a logarithmic an exponential n 11 10 8 9 10 11 12 function with a its domain of and the end behavior on the RIGHT side is as VIOLO asymptote of The end behavior on the LEFT side is as www examp The range of the function is

The Venn diagram here shows the cardinality of each set Use this to find the probability of observing the given set A 13 C 11 B

missing cumulative value identified by asterisk Bin Frequenc Cumulative y 1 5 6 6 2 12 8 41 6 70 4 99 2 More A 60 00 B 5 00 C 100 5 00 30 00 60 00 100 00 4

Exponential Functions 1 A baker records the internal temperature of a pie that has been left to cool on a counter The room temperature is 14 C An equation that models this situation is T t 68 0 5 1 14 where T is the temperature in degrees Celsius and is the time in minutes a Sketch the graph of the function 9 14 H A y 14 y in 82 b Determine the i Domain TEIR ii Range yeir y 14 c Determine the temperature to the nearest degree of the pie after 15 minutes 15 r 68 0 5 110 k T 38004 682 14 d How much time did it take for the pie to reach an internal temperature of 31 C

1 2 2 5 b the line B At least one of the answers above is NOT correct For the equation y 2 5 3 a the y intercept is 1 2 and the slope is 2 5 A is horizontal O B slopes upward C slopes downward D none of the above 1 2 2 5 B

Give graphic representations of a Empirical rule for 20 30 b Standard normal distribution c P a x b d Normal distribution with different standard deviations but same n e Standard normal distribution in a one tailed versus a two tailed te f Student t distribution with large degrees of freedom

Use the grid to draw the graph of each line 12 y 3x 1 13 y 2x 3 14 y x 122 C 1 15 y 1 5x 1430 d e f

Suppose you collect a dataset with mean 7 and standard deviation 2 Ifx represents each data value in the data set and new data values are created using the transformation y 2x 1 what will be the mean and standard deviation of y mean 15 standard deviation 2 mean 15 standard deviation 4 mean 14 standard deviation 4

You can convert temperatures in degrees Celsius to degrees Fahrenheit using the formula F 9 5 C 32 If a sample of temperatures in Celsius has a mean 30 and standard deviation 4 the mean and standard deviation in Fahrenheit will be mean 86 standard deviation 7 2 mean 54 standard deviation 7 2 mean 86 standard deviation 4

A sample of size 110 is selected from a population with p 0 60 a What is the expected value of p b What is the standard error of p Round your answer to four decimal places c Show the sampling distribution of p 2 1 0 1 2 0 10 0 05 0 00 0 05 3 0 10 P P 0 05 0 00 0 05 0 10 0 15 P 0 50 0 55 0 60 0 65 0 70

4 Match the following given inequalities with their corresponding solutions 32 122 15 2z 539 52 853 3z 5216 DRAG DROP THE ANS z 14 27 9 25

What is the value of x in the following equation 3 1 1 42 8 2 1 3 A B 2 D C 6 6

In the diagram which one has a positive slope A AB B DB AC C 8

c What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii Let a success be that someone from the Hawaii plant is in the sample of employees who fill out the questionnaire Previously we found the probabilities of exactly x 0 successes f 0 and exactly x 1 success f 1 To find the desired probability that 2 or more employees in this sample work in the Hawaii plant there will be x Select successes Therefore the probability will be calculated as Select f 3 f 2 f 3 f 4 f 15 f 2 f 3 f 15 Submit Skip you cannot come back

A simple random sample of size n 36 is obtained from a population that is skewed right with u 72 and 18 a Describe the sampling distribution of x b What is P x 76 65 c What is P x 65 85 d What is P 69 75 x 78 9 a Choose the correct description of the shape of the sampling distribution of x O A The distribution is uniform OB The distribution is skewed left OC The distribution is skewed right OD The distribution is approximately normal O E The shape of the distribution is unknown Find the mean and standard deviation of the sampling distribution of X Px ox Type integers or decimals Do not round b P x 76 65 Round to four decimal places as needed c P x 65 85 Round to four decimal places as needed d P 69 75 x 78 9 Round to four decimal places as needed

At a clothing store Ted bought 4 shirts and 2 ties for a total price of 95 At the same time store Stephen bought 3 shirts and 3 ties for 84 Each shirt was the same price and each tie was the same price Which system of equations can be used to find s the cost of each shirt in dollar and t the cost of each tie in dollars A B 6 s t 95 3 s t 84 4s 2t 95 3s 3t 84 7s 5t 179 s t 12 7s 5t 179 7s 5t 12 s t

Write the equation of the line passing through points 2 2 and 1 0 in slope intercept form

Solve 12z 72 and then plot the solution set on the number line

1 7 Which ratio forms a proportion with 14 A B D E 9 5 12 22 42 36 Select all that apply

Age at first marriage The National Survey of Family Growth conducted by the Centers for Disease Control gathers information on family life marriage and divorce pregnancy infertility use of contraception and men s and women s health One of the variables collected on this survey is the age at first marriage The average age at first marriage among 5932 women is 22 3 with a standard deviation of 4 3 NSFG 2010 Construct a 84 confidence interval to estimate the average age at first marriage of women and write a sentence interpreting this interval 84 confidence interval Round to two decimal places Interpretation O The researchers can be 84 confident that the sample mean of the ages at their first marriage is in this confidence interval O The researchers can be 84 confident that the true mean age of all women at their first marriage is in this confidence interval O 84 of women have their first marriage when their age is within our confidence interval O There is 84 chance that true mean is in this confidence interval

Assume that a sample is used to estimate a population proportion p Find the 80 confidence interval for a sample of size 224 with 199 successes Enter your answer as an open interval i e parentheses using decimals not percents accurate to three decimal places 80 C I

In right triangle ABC side c 22 and m A 40 Find the lengths of side a and side 6 Round answers to the nearest tenth an 18 5 X b 28 7 X

a x Special triangles Write answers in simplest radical form b 6 y y 60 V 30 21 8 5 V V y X 60 X 5 2 y

a x special triangles Write answers in simplest radical form b 2 3 X y 45 y UI 45 V 21 4 6 V c P X y 6 45 6

In right triangle ABC side a 43 and m A 65 Find the lengths of side band side c c is the hypotenuse Round answers to the nearest tenth b C

Solve for Leave answer in simplified radical form X x 45 5

Find the values of x and y Round answers to the nearest tent 12 cm 80

31 Exercise and type 2 diabetes It is generally accepted that regular exercise provides health benefits to indi viduals with type 2 diabetes although the exact exercise regimen aerobic vs resistance vs both is unclear The subjects in this study were sedentary 30 to 75 year old adults with type 2 diabetes and elevated hemoglobin Alc levels above 6 5 The level of hemoglobin Alc correlates very well with a person s recent overall blood sugar levels If the blood sugars have generally been run ning high during the previous few months the level of hemoglobin Alc will be high In a randomized con trolled study 41 subjects were assigned to a nonexer cise control group 73 to resistance training only 72 to aerobic exercise only and 76 to combined aerobic and resistance training The weekly duration of exercise was similar for all three exercise groups and subjects remained on the exercise regimens for nine months At the end of nine months the hemoglobin A1c levels of

For each problem select the best response a A researcher wishes to determine whether the rate of water flow in liters per second over an experimental soil bed can be used to predict the amount of soil washed away in kilograms In this study the explanatory variable is the A size of the soil bed OB rate of water flow OC amount of eroded soil OD depth of the soil bed O E None of the above b The Columbus Zoo conducts a study o determine whether a household s income can be used to predict the amount of money the household will give to the zoo s annual fund drive The response variable in this study is OA a household s income OB all households in Columbus C the Columbus Zoo O D the amount of money a household gives to the zoo s annual fund drive OE None of the above c A researcher measures the correlation between two variables This correlation tells us OA whether a cause and effect relation exists between two variables OB whether or not a scatterplot shows an interesting pattern OC the strength of a straight line relation between two variables OD whether there is a relation between two variables E None of the above

Fifty four wild bears were anesthetized and then their weights and chest sizes were measured and listed in a data set Results are shown in the accompanying display Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes When measuring an anesthetized bear is it easier to measure chest size than weight If so does it Determine the null and alternative hypotheses Ho P H p 0 Type integers or decimals Do not round Identify the correlation coefficient r r Correlation Results Correlation coeff r 0 950958 Critical r 0 2680855 P value two tailed 0 000 0 Round to three decimal places as needed

Use the given data set to complete parts a through c below Use 0 05 13 8 74 9 8 78 X y Click here to view a table of critical values for the correlation coefficient A a Construct a scatterplot Choose the correct graph below Ay 10 8 10 9 15 6 4 2 0 0 4 1 8 8 13 X 8 12 16 OB Ay 10 8 6 4 2 0 0 4 8 12 16 o 11 9 26 14 8 11 OC Ay 10 8 6 N 4 2 0 0 4 6 6 14 X OA There is insufficient evidence to support the claim of a nonlinear correlation between the two variables B There is sufficient evidence to support the claim of a nonlinear correlation between the two variables OC There is insufficient evidence to support the claim of a linear correlation between the two variables 8 12 16 Q 4 3 11 12 9 13 OD Ay 10 8 6 4 2 0 0 4 b Find the linear correlation coefficient r then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables The linear correlation coefficient is r 0 817 Round to three decimal places as needed 8 12 16 7 7 26 Q 5 4 7 Using the linear correlation coefficient found in the previous step determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables Choose the correc answer below

When making predictions based on regression lines which of the following is not listed as a consideration Choose the correct answer below OA Use the regression equation for predictions only if the graph of the regression line on the scatterplot confirms that the regression line fits the points reasonably well OB Use the regression equation for predictions only if the linear correlation coefficient r indicates that there is a linear correlation between the two variables OC Use the regression line for predictions only if the data go far beyond the scope of the available sample data OD If the regression equation does not appear to be useful for making predictions the best predicted value of a variable is its

Fill in the blank is the For a pair of sample x and y values the difference between the observed sample value of y and the y value that is predicted by using the regression equation For a pair of sample x and y values the is the difference between the observed sample value of y and the y value that of ya is predicted by using the regression equation

Which of the following is not equivalent to the other three Choose the correct answer below O Explanatory variable O Predictor variable O Dependent variable O Independent variable

You really struggle remembering to bring your lunch to work Each day seems to be independent as to whether you remember to bring your lunch or not The chance that you forget your lunch each day is 39 1 Consider the next 46 days Let X be the number of days that you forget your lunch out of the 46 days Calculate the following Hx 17 98 ox 10 95 P X 18 11 98 P X 23 P X 14 P 16 X 19

Suppose the mean starting salary for nurses is 66 239 nationally The standard deviation is approximately 10 660 The starting salary is not normally distributed but it is mound shaped A sample of 40 starting salaries for nurses is taken State the random variable O The standard deviation of starting salaries of nurses O The mean starting salary of a nurse Starting salary for a nurse What is the mean of the sample mean H 66 239 What is the standard deviation of the sample mean Round to two decimal places 0 1685 49 What is the shape of the sampling distribution of the sample mean Why O You can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 30 O You can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30 O You can t say anything about the sampling distribution of the sample mean since the population of the random variable is not normally distributed and the sample size is greater than 30 Find the probability that the sample mean is more than 72 000 Round to four decimal places P X 72000 Find the probability that the sample mean is less than 59 000 Round to four decimal places

Refer to the table below Given that 2 of the 149 subjects are randomly selected complete parts a and b Group Type Rh Rh 0 49 11 A 40 9 B 20 3 AB 15 2 a Assume that the selections are made with replacement What is the probability that the 2 selected subjects are both group AB and type Rh Round to four decimal places as needed

2 The following data set was collected from a survey Yes No No No Yes Yes No Yes No No Yes No No Yes No What is the relative frequency of the No class Answer Continue Reset answer

J and K are independent events P J K 0 22 Find P J P J 0 22

If a couple were planning to have three children the sample space summarizing the gender outcomes would be bbb bbg bgb bgg gbb gbg ggb ggg a Construct a similar sample space for the possible eye color outcomes using b for blue eyed and g for green eyed of two children b Assuming that the outcomes listed in part a were equally likely find the probability of getting two green eyed children c Find the probability of getting exactly one blue eyed child and one green eyed child a What is the sample space Use a comma to separate answers as needed

Giving a test to a group of students the grades and gender are summarized below A C Male 7 17 13 Female 4 12 9 Total 11 29 22 B Total 37 25 62 If one student is chosen at random Find the probability that the student was male 59 67 Find the probability that the student was male AND got a B 45 94 Find the probability that the student was male OR got an C If one student is chosen at random find the probability that the student got a C GIVEN they are mal