Statistics Questions

90 The average length of a maternity stay in a U S hospital is said to be 2 4 days with a standard deviation of 0 9 days We randomly survey 80 women who recently bore children in a U S hospital a In words X b In words X c X d In words EX e EX f Is it likely that an individual stayed more than five days in the hospital Why or why not g Is it likely that the average stay for the 80 women was more than five days Why or why not h Which is more likely I An individual stayed more than five days ii The average stay of 80 women was more than five days i If we were to sum up the women s stays is it likely that collectively they spent more than a year in the hospital Why or why not

than percents In a family with 5 children what is the probability of having 3 boys and then 2 girls in that order Exclude multiple births and assume all outcomes are equally likely In a family with 5 children what is the probability of having 3 boys and 2 girls in any order Exclude multiple births and assume all outcomes are equally likely

75 Salaries for entry level managers at a restaurant chain are normally distributed with a mean of 44 000 and a standard deviation of 6 500 We randomly survey 10 managers from these restaurants a In words X b X c In words EX d EX e Find the probability that the managers earn a total of over 400 000 f Find the 90th percentile for an individual manager s salary g Find the 90th percentile for the sum of ten managers salary h If we surveyed 70 managers instead of ten graphically how would that change the distribution in part d i If each of the 70 managers received a 3 000 raise graphically how would that change the distribution in part b

The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 52 while 36 require a developmental math course and 30 require a developmental English course Find the probability that a first year student requires both a development math course and a developmental English course

You own 15 CDs You want to randomly arrange 7 of them in a CD rack What is the probability that the ra ends up in alphabetical order The probability that the CDs are in alphabetical order is

Find the value of 7C3 35 O24 0 210 O 5 040

A pianist plans to play 4 pieces at a recital from her repertoire of 23 pieces How many different recital programs are possible

A four person committee is to be selected from an organization s membership of 20 people How many different committees are possible

A pianist plans to play 4 pieces at a recital In how many ways can she arrange these pieces in the program Your answer is

Compute the value of

Find the value of 7 P3 O 5 040 O 24 0 210 35

A restaurant offers a choice of 6 salads 12 main courses and 7 desserts How many possible 3 course meals are there

Standard automobile license plates in a country display 2 numbers followed by 3 letters followed by 2 numbers How many different standard plates are possible in this system Assume repetitions of letters and numbers are allowed Your answer is

A die is rolled twice What is the probability of showing a 1 on the first roll and an even number on the second roll Your answer is

A survey of 138 persons was conducted at TCC and it was found that 10 persons carried a cell phone 97 persons carried a tablet computer and 7 carried both a cell phone and a tablet 1 How many people carried a cell phone or a tablet 2 How many people carried neither a cell phone nor a tablet 3 How many people carried a cell phone only 4 How many people carried a tablet but not a cell phone

The NIH is creating a test for the Flu virus The incidence of a Flu is low 2 percent in the general population There is a trial version but it sometimes misses the disease The probability of a false negative is 3 percent Similarly someone who does not have the Flu will sometimes get a positive reading The probability of this is 30 percent Fill in the tree diagram and Answer in percent to 2 decimal places Marginal Probabilities P D P no D Conditional Probabilities P positive D P negative D P positive no D False negative False Positive Joint Probabilities P D and positive P D and negative P no D and positive P negative no D Calculate the probability that a positive test result means someone has the Flu P no D and negative

The NIH is creating a test for the Covid virus The incidence of a Covid is low 10 percent in the general population There is a trial version but it sometimes misses the disease The probability of a false negative is 3 percent Similarly someone who does not have Covid will sometimes get a positive reading The probability of this is 30 percent Fill in the tree diagram and Answer in percent to 2 decimal places Marginal Probabilities P D P no D Conditional Probabilities P positive D P negative D P positive no D False negative False Positive Joint Probabilities P D and positive P D and negative P no D and positive P negative no D Calculate the probability that a positive test result means someone has Covid P no D and negative

A survey asks Which online services have you used in the last month Twitter Facebook Have used both The results show 33 of those surveyed have used Twitter 59 have used Facebook and 8 have used both What percent of the people surveyed used neither Twitter nor Facebook

An urn contains 7 blue 5 yellow and 3 gray marbles Two marbles are randomly drawn from the urn Find the probability the two marbles are the same color O 83 225 O 68 225 O 68 210 03040

Suppose you roll a special 7 sided die What is the probability that the number rolled is a 1 OR a 2

The z value corresponding to a 0 80 cumulative probability was found to be 0 84 Thus the necessary return x will be 0 84 standard deviations above the mean return Recall the formula t convert a given value x to the standard normal random z Z x x 0 Here we have the values of z and o but need to find x Solve the equation for x

c Assume that the class has 80 students and that the examination period is 130 minutes in length How many students do you expect will be unable to complete the exam in the allotted time Before finding the number of students who will be unable to complete the exam in 130 minutes first find the probability that any student does not complete the exam in 130 minutes If the student does not finish the exam in the first 130 minutes then it will take more than 130 minutes to complete As a probability statement completing the exam in more than 130 minutes is P x 7130 First convert the random variable x 130 to a normal random variable z Recall that the mean was given to be 100 minutes and the standard deviation was given to be a 20 minutes Z x O 130 100

The area under the curve to the left of z 2 was found to be 0 0228 and the area under the curve to the left of z 0 75 was found to be 0 2266 The area under the curve between these two values will be the difference of the larger area minus the smaller area Therefore the desired probability that a student will complete the exam in more than 60 minutes but less than 85 minutes is calculated as follows P 60 x 85 P 2 z 0 75 P Z 0 75 P Z 2 0 2266

Calculate the standard deviation of the sample data shown to two decimal places X 14 3 27 7 28 8 24 3 18 8 11 2 7 6

89 Salaries for managers in a restaurant chain are normally distributed with a mean of 44 000 and a standard deviation of 6 500 We randomly survey 10 managers from that district a Find the 90th percentile for an individual manager s salary b Find the 90th percentile for the average manager s salary

84 Find the probability that the average price for 30 gas stations is less than 4 55 a 0 6554 b 0 3446 c 0 0142 d 0 9858 0 0

Using the standard normal z random variable the probability statement P 60 x 85 is now P 2 z 0 75 so the normal probability table can be used The area to the left of 2 is Select than the area to the left of 0 75 Therefore the probability of P 2 z 0 75 will be calculated as Select The area under the curve to the left of z 2 was found to be 0 0228 Use the table excerpt below to find the area under the curve to the left of z 0 75 P Z 0 75 to four decim places 0 00 0 2119 0 2420 0 2743 Z 0 8 0 7 0 6 P Z 0 75 0 01 0 2090 0 2389 0 2709 0 02 0 2061 0 2358 0 2676 0 06 0 07 0 08 1949 0 1922 0 1894 0 05 0 1977 0 2266 0 2236 0 2206 0 2177 0 2578 0 2483 0 2546 0 2514 0 03 0 2033 0 04 0 2005 0 2296 0 2327 0 2611 0 2643 0 09 0 1867 0 2148 0 2451

85 Suppose in a local kindergarten through 12th grade K 12 school district 53 percent of the population favor a charter school for grades K through five A simple random sample of 300 is surveyed Calculate the following using the normal approximation to the binomial distribtion a Find the probability that less than 100 favor a charter school for grades K through 5 b Find the probability that 170 or more favor a charter school for grades K through 5 c Find the probability that no more than 140 favor a charter school for grades K through 5 d Find the probability that there are fewer than 130 that favor a charter school for grades K through 5 e Find the probability that exactly 150 favor a charter school for grades K through 5 If you have access to an appropriate calculator or computer software try calculating these probabilities using the technology decided to carpool together to get to school Each day

distributed uniformly from zero to 75 minutes One hundred riders are randomly sampled to learn how long they waited 81 The 90th percentile sample average wait time in minutes for a sample of 100 riders is a 315 0 b 40 3 c 38 5 d 65 2

45 of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder Among Latino California registered voters 57 5 prefer life in prison without parole over the death penalty for a person convicted of first degree murder 36 3 of all Californians are Latino These preferences are summarized in the contingency table below Latino 0 25875 0 10425 0 363 Total 0 45 0 55 1 Suppose that one Californian is randomly selected Let C represent Prefer Life Sentence and I represent Latino Round your answers to parts a and b to two decimal places a What is P C Prefer Life Sentence Prefer Death Penalty Total Non Latino 0 19125 0 44575 0 637 b What is P CL c Are C and L independent events O Yes because P C and P CIL are equal O No because P C and P CIL are not equal

Recall that the standard normal random variable z represents the number of standard deviations a value x is away from the mean The normal probability table gives area under the curve to the left of a given z value also called the cumulative probability Use the table to find the value of zo corresponding to a 0 80 cumulative probability rounding the result to two decimal places P z Szo 0 80 Zo

c How big does the return have to be to put a domestic stock fund in the top 20 for the three year period Another way to think about this question is in terms of probability instead of percentage To have a domestic stock fund in the top 20 means that 80 of domestic stock funds will be less than some value First convert 80 to a probability probability B percentage 100 100 Here we are working backwards to find a return such that if new large cap domestic stock fund was randomly selected the probability the new fund has a return less than this value is

Step 8 To find P 1 65 z 1 05 subtract the area to the left of z 1 65 from the area to the left of z 1 05 Use the following table excerpt 0 08 0 09 Z 1 7 0 0375 0 0367 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 0446 0 0436 0 0427 0 0418 0 0409 0 0401 0 0392 0 0384 1 6 0 0548 0 0537 0 0526 0 0516 0 0505 0 0495 0 0485 0 0475 0 0465 0 0455 1 5 0 0668 0 0655 0 0643 0 0630 0 0618 0 0606 0 0594 0 0582 0 0571 0 0559 Use the table excerpt above to find the area under the standard normal curve to the left of z 1 65 P Z 1 65 P z 1 65 Z 1 1 1 0 0 9 0 00 0 01 0 1357 0 1335 0 1587 0 1562 0 1841 0 1814 0 02 0 1314 0 1539 0 1788 0 03 0 1292 0 1515 0 1762 0 04 0 1271 0 1492 0 1736 0 08 0 09 0 06 0 07 0 1230 0 1210 0 1446 0 1423 0 1190 0 05 0 1251 0 1469 0 1711 0 1685 0 1660 0 1635 0 1611 0 1170 0 1401 0 1379 Use the table excerpt above to find the area under the standard normal curve to the left of z 1 05 P Z 1 05 P Z 1 05

The desired probability is P 60 x 85 First convert this probability statement using the standard random variable z Recall the formula for this conversion below where x is the value that needs to be converted is the population mean and o is the population standard deviation Z We found the z value that corresponds to x 60 to be z 2 Find the z value that corresponds to x 85 with mean 100 and standard deviation o 20 x x 0 6 85 100

The probability statement was determined to be P z 0 14 Recall that the normal probability table gives the area under the curve to the left of a given z value An excerpt is given below Z 0 00 0 01 0 02 0 03 0 04 0 0 0 5000 0 5040 0 5080 0 5120 0 5160 0 05 0 06 0 07 0 1 0 5398 0 5438 0 5478 0 5517 0 5557 0 5596 0 5636 0 2 0 5793 0 5832 0 5871 0 5910 0 08 0 5199 0 5239 0 5279 0 5319 0 09 0 5359 0 5675 0 5714 0 5753 0 5948 0 5987 0 6026 0 6064 0 6103 0 6141 Use the above table to find the probability of completing the exam in an hour or less P z 0 14 rounding the result to four decimal places P z 0 14

The correct size of a nickel is 21 21 millimeters Based on that the data can be summarized into the following table indicating the numbers of children from each income group who drew the nickel too small and too large Low Income High Income Total Too Small 8 8 16 Too Large 12 7 19 Total 20 15 35 Based on this data give your answers as fractions or decimals to at least 3 decimal places a The proportion of children from the low income group that drew the nickel too large is b The proportion of children from the high income group that drew the nickel too large is c The proportion of all children that drew the nickel too large is d If a child is picked at random what is the probability they are in the low income group given they drew the nickel too large e If a child is picked at random what is the probability they are in the high income group OR drew the

A CBS News poll conducted June 10 and 11 2006 among a nationwide random sample of 651 adults asked those adults about their party affiliation Democrat Republican or none and their opinion of how the US economy was changing getting better getting worse or about the same The results are shown in the table below better same worse 38 104 44 12 87 137 21 90 118 Express each of your answers as a percent rounded to the nearest tenth for example 12 3 Republican Democrat none a What percent of survey respondents identified themselves as affiliated with neither party b What percent of survey respondents thought the economy was about the same c What percent of those affiliated with neither party thought the economy was about the same d Among survey respondents who thought the economy was about the same what percent were affiliated with neither party 06

The correct size of a certain object is 21 21 millimeters Based on that the data can be summarized into the following table indicating the numbers of children from each group who drew the certain object too small and too large Group 1 Group 2 Total Too Small 8 8 16 Too Large 12 7 19 Total 20 15 35 Based on this data give your answers as fractions or decimals to at least 3 decimal places a The proportion of children from group 1 that drew the object too large is b The proportion of children from group 2 that drew the object too large is c The proportion of all children that drew the object too large is d If a child is picked at random what is the probability they are in group 1 given they drew the object too large e If a child is picked at random what is the probability they are in group 2 OR drew the object too large

A recent study surveyed 1 341 households asking if the residents rented or owned and if the residents included dependents The results are summarized below 1 or More Dependent No Dependents Total 188 664 Renter 677 Total 857 1 341 a What number of households reported having 1 or more dependent and renting Fill in the missing entry in the table b What percent of the renters reported having no dependents Answer to 1 decimal place Homeowner 476 296 484 c Someone uses the table and calculates percent 188 484 38 8 Which is the correct interpretation of this O 38 8 of homeowners reporting having no dependents O 38 8 of people with no dependents reported being homeowners O 38 8 of people surveyed were homeowners with no dependents O None of these are correct

Phi Delta Kappa PDK is an international professional organization for educators that in collaboration with Gallup has been conducting polls on the public s attitudes toward the public schools since 1969 The following was one of the questions on the most recent poll conducted June 4 13 2011 Most teachers in the nation now belong to unions or associations that bargain over salaries working conditions and the like Has unionization in your opinion helped hurt or made no difference in the quality of public school education in the United States The respondents answers broken down by party affiliation is shown below Republican Democrat Independent Helped Hurt 35 197 52 6 Made no difference Don t know refused Which of the following statements is correct 146 78 105 12 69 178 90 4 O A histogram or a box plot would be useful to investigate if distribution of opinion on teachers belonging to unions or bargaining associations varies by political party affiliation O The results of the survey suggest a relationship between opinion on teachers belonging to unions or bargaining associations and political party affiliation O 14 of Republicans and 58 of Democrats think that teachers belonging to unions or bargaining associations helped the quality of public school education in the United States O The results of the survey suggest that opinion on teachers belonging to unions or bargaining associations and political party affiliation are independent

Every cereal box has a gift inside but you cannot tell from the outside what the gift is The store manager assures you that 13 of the 60 boxes on the shelf have the secret decoder ring The other 47 boxes on the shelf have a different gift inside If you randomly select two boxes of cereal from the shelf to purchase what is the probability that BOTH of them have the secret decoder ring Give answer as a decimal correct to four decimal places probability

Giving a test to a group of students the grades and shirt colors are summarized below A B Red Shirt 19 3 Blue Shirt 14 2 C Total 35 33 68 13 17 Total 17 21 30 If one student is chosen at random a Find the probability that the student has a Red Shirt GIVEN they got a C Round to 4 decimal places if needed b Find the probability that the student got a C GIVEN they are wearing a Red Shirt Round to 4 decimal places if needed

Calculate the 45th percentile of the data shown X 5 8 9 14 6 14 8 16 5 19 2 19 9 21 1 24 5

67 Determine which of the following are true and which are false Then in complete sentences justify your answers a When the sample size is large the mean of X is approximately equal to the mean of X b When the sample size is large X is approximately normally distributed c When the sample size is large the standard deviation of X is approximately the same as the standard deviation of X

Here is a data set 89 63 58 51 54 51 63 57 75 64 62 68 60 84 85 67 52 71 67 57 73 57 67 65 68 74 60 68 55 64 70 You are examining 5 12457778 6 7 01345 the data with a stem and leaf plot Here is the start of the 00233445777888

Sales 8 7 6 5 4 3 2 1 Wed Thur Q The plot above shows the number of computers a store sold the first four days of this wee How many computers did they sell altogether these four days Mon Tue

72 Which of the following is NOT true about the theoretical distribution of sums a The mean median and mode are equal b The area under the curve is one c The curve never touches the x axis d The curve is skewed to the right

that oration Phi Delta Kappa PDK is an international professional organization for edu Gallup has been conducting polls on the public s attitudes toward the public schools since 1969 The following was one of the questions on the most recent poll conducted June 4 13 2011 Most teachers in the nation now belong to unions or associations that bargain over salaries working conditions and the like Has unionization in your opinion helped hurt or made no difference in the quality of public school education in the United States The respondents answers broken down by party affiliation is shown below Republican Democrat Independent Helped Hurt Made no difference Don t know refused 35 197 52 6 Calculate P Republican Helped 146 78 105 12 Round your probabilities to 4 decimal places as needed Calculate P Republican 69 178 90 4 Using your answers above are believing that unionization helped the quality of public school education in the United States independent or dependent of being Republican Being Republican and believing that unionization helped the quality of public school education are O DEPENDENT since P Republican P Republican Helped O INDEPENDENT since P Republican P Republican Helped Republican P Republican Helped

Write the given number using prime factorization Write your answer using Exponential Notation For instance 98 2 7 2 Instructions Find the prime factorization of 6

Enter the prime factorization of 77 Use exponents for repeated factors Be sure to use the between different factors For example the pr factorization for 12 can be entered as 2 2 3 or 3 2 2