Statistics Questions

d the area of the shaded region The graph to the right depicts IQ scores of adults and those scores are normally distributed with a mean of 100 and a standard deviation of 15 k10 view page 1 of the table Click to view page 2 of the table dard Normal Table Page 2 Standard Normal 2 Distribution Cumulative Area from the LEFT 00 5000 5318 KTP9 4554 6916 COPEN 7530 2001 8159 849 5032 9102 9332 9452 9554 9641 9713 9772 9861 0891 9918 9938 9953 01 5040 5438 5832 6217 6591 6950 7291 7611 7910 4106 8438 8665 8869 9049 9207 9345 9463 9564 9649 9719 9778 9826 9864 9896 9920 9940 9955 02 5080 5478 5871 6255 6628 6985 7324 7939 8212 8461 8686 8888 9066 9222 9357 9474 9573 9656 9726 9783 9830 9868 9898 9922 9941 9956 POSITIVE z Scores 03 5120 5517 5910 6293 6664 2019 7357 7673 7967 8238 8485 8708 8907 9082 9236 9370 9484 9582 9664 9732 9788 9834 9871 9901 9925 9943 9957 04 5160 5557 5948 6331 6700 7054 7389 7704 7995 8264 8508 8729 8925 9099 9251 9382 9495 9591 9671 9738 9793 9838 9875 9904 9927 9945 9959 05 5199 5596 5987 6368 6736 7088 7422 7734 8023 8289 8531 8749 8944 9115 9265 9394 9505 9599 9678 9744 9798 9842 9878 9906 9929 9946 9960 06 5239 5636 6026 6406 6772 7123 7454 7764 8051 8315 8554 8770 8962 9131 9279 9406 9515 9608 9686 9750 9803 9846 9881 9909 9931 9948 9961 07 5279 5675 6064 6443 6808 7157 7486 7794 8078 8340 8577 8790 8980 9147 9292 9418 9525 9616 9693 9756 9808 9850 9884 9911 9932 08 5073 5319 5714 6103 6480 6844 7190 9761 9812 9854 9887 9913 9934 9949 9951 99629963 7517 7823 8106 8365 8599 6810 8997 9162 9306 9429 9535 9625 9699 5077 09 5359 5753 6141 6517 6879 7224 7549 7852 8133 8389 8621 6830 9015 9177 9319 9441 9545 9633 9706 9767 9817 9857 9890 9916 9936 9952 9964 9974 X Standard Normal Table Page 1 NEGATIVE Z Scores 2 3 50 and lower 34 33 32 31 3 0 2 9 2 8 2 7 26 2 5 24 23 2 2 21 20 19 1 8 17 1 6 15 1 4 13 12 11 10 0 9 0 8 0 7 Standard Normal 2 Distribution Cumulative Area from the LEFT 00 0001 0003 0005 0007 0010 0013 0019 0026 0035 0047 0062 0082 0107 0139 0179 0228 0287 0359 0446 0548 0668 0808 0968 1151 1357 1587 1841 2119 2420 01 0003 0005 0007 0009 0013 0018 0025 0034 0045 0060 0080 0104 0136 0174 0222 0281 0351 0436 0537 0655 0793 0951 1131 1335 1562 1814 2090 2389 02 0003 0005 0006 0009 0013 0018 0024 0033 0044 0059 0078 0102 0132 0170 0217 0274 0344 0427 0526 0643 0778 0934 1112 1314 1539 1788 2061 2358 03 0003 0004 0006 0009 0012 0017 0023 0032 0043 0057 0075 0099 0129 0166 0212 0268 0336 0418 0516 0630 0764 0918 1093 1292 1515 1762 2033 2327 04 0003 0004 0006 0008 0012 0016 0023 0031 0041 0055 0073 0096 0125 0162 0207 0262 0329 0409 0505 0618 0749 0901 1075 1271 1492 1736 2005 2296 05 0003 0004 0006 0008 0011 0016 0022 0030 0040 0054 0071 0094 0122 0158 0202 0256 0322 0401 0495 0606 0735 0885 1056 1251 1469 1711 1977 2266 06 0003 0004 0006 0008 0011 0015 0021 0029 0039 0052 0069 0091 0119 0154 0197 0250 0314 0392 0485 0594 0721 0869 1038 1230 1446 1685 1949 2236 07 0003 0004 0005 0008 0011 0015 0021 0028 0038 0051 0037 0049 0068 A 0066 0087 0089 20116 0113 0150 0146 0192 0188 0244 0239 0301 0375 0465 0571 0694 0838 1003 3190 3401 1635 1894 2177 0307 0384 0475 0582 08 0708 0853 3020 1210 1423 1660 1922 2206 0003 0004 0005 0007 0010 0014 0020 0027 09 0002 0003 0005 0007 10010 0014 0019 0026 0036 0048 0064 0084 0110 0143 0183 0233 0294 0367 0455 0559 0681 0823 0985 3170 1379 1611 1867 2148 X mainin

The probability that a student at a particular college is a male is 0 43 The probability that a student at this college is a biology major is 0 16 while the probability that a student at this college is a biology major and male is 0 28 The probability that a randomly selected student this college is male or a biology major is 00 99 00 63 O 0 31 O 0 43

A recent campus poll found that 30 of all students at IRSC are history majors Determine the probability that 10 or 15 students out of a random sample of 21 students are history majors Use the Binomial probability formula or the binomial probability table if possible to solve 0 567 0 3987 0 0142 0413

The probability that a student is dual enrolled is 0 16 Suppose two students are chosen at random Determine the probability that the first student selected is dual enrolled and the second student selected is not dual enrolled Hint these two events are independent 0 7056 0 3888 O 0 1344 0256

A recent poll found that 36 of all registered voters in Okeechobee County support a proposed new property tax Determine the probability that all people out of a random sample of 5 people support this proposed new property tax Use the Binomial probability formula or the binomial probability table if possible to solve 0 006 0 0754 00 1518 9698

The total number of possible outcomes for 4 rolls of a eight sided die is O 512 O 32 O 4096 O24

The sum of the probabilities of all simple events of any experiment must always equal 00 OF Oo

Use the data below to determine the logarithmic regression for the value of a retirement account over 50 years Then estimate the value of the retirement account on the 60th year Round your answer to the nearest whole number Years 1 10 20 30 40 50 Retirement thousand 10 52 78 82 96 100

Question 4 Studies show that 18 of all credit card holders eventually become delinquent Determine the probabilit that exactly 5 people out of a random sample of 16 people will eventually become delinquent Use the Binomial probability formula or the binomial probability table if possible to solve 00 7845 0 0305 O 0 7062 O 0 093

In a group of 136 students 116 are freshmen If one student is selected at random the probability that this student is not a freshman is O 0 147 O 0 852 O 0 713 O 0 497

If a six sided die is rolled once the probability of obtaining a number greater than 1 is O 0 54 O 0 83 O 0 92 0 09

The intersection of two events A and B is composed of the outcomes that are O common to both A and B O either in A or B but not both O either in A or B including the outcomes in in both A and B not common to both A and B

Question 3 In an upcoming national swim competition 11 swimmers will be competing How many different ways can 2 swimmers finish the competition first and second 09 0110

Which of the following statements is true for the probability distribution of a discrete random variable 00 P z 1 o P z 1 OP z 1 OP x 0

In classical probability O probability is assigned to an outcome using personal beliefs feelings and judgements all simple events are equally likely O all events are conditional O probability is calculated using relative frequencies derived from empirical data

A random sample of 863 births in a state included 422 boys Construct a 95 confidence interval estimate of the proportion of boys in all births It is believed that among all births the proportion of boys is 0 508 Do these sample results provide strong evidence against that belief Construct a 95 confidence interval estimate of the proportion of boys in all births 0 456 p 0 522 Round to three decimal places as needed Do these sample results provide strong evidence against that belief OA There is strong evidence against 0 508 as the value of the proportion of boys in all births because 0 508 is contained within the 95 confidence interval OB There is not strong evidence against 0 508 as the value of the proportion of boys in all births because 0 508 is not contained within the 95 confidence interval OC There is not strong evidence against 0 508 as the value of the proportion of boys in all births because 0 508 is contained within the 95 confidence interval OD There is strong evidence against 0 508 as the value of the proportion of boys in all births because 0 508 is not contained within the 95 confidence interval

chere to view a t distribution table chere to view page 1 of the standard normal distribution table there to view page 2 of the standard normal distribution table is the confidence interval estimate of the population mean F d to three decimal places as needed Critical t values Critical t value negative Left tail Right tail Degrees of Freedom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 t Distribution Critical t Values 0 005 0 01 63 657 9 925 5 841 4 604 4 032 3 707 3 499 3 355 3 250 3 169 3 106 3 055 3 012 2 977 2 947 2 921 2 898 2 878 2 861 2 845 2 831 2 819 0 01 0 02 31 821 6 965 4 541 3 747 3 365 3 143 2 998 2 896 2 821 2 764 2 718 2 681 2 650 2 624 2 602 2 583 2 567 2 552 2 539 2 528 2 518 2 508 Area in One Tail 0 025 Area in Two Tails 0 05 12 706 4 303 3 182 2 776 2 571 2 447 2 365 2 306 2 262 2 228 2 201 2 179 2 160 2 145 2 131 2 120 2 110 2 101 2 093 2 086 2 080 2 074 0 050 0 05 0 10 6 314 2 920 2 353 2 132 2 015 1 943 1 895 1 860 1 833 1 812 1 796 1 782 1 771 1 761 1 753 1 746 1 740 1 734 1 729 1 725 1 721 1 717 1 714 0 10 0 20 3 078 1 886 1 638 1 533 1 476 1 440 1 415 1 397 1 383 1 372 1 363 1 356 1 350 1 345 1 341 1 337 1 333 1 330 1 328 1 325 1 323 1 321 1 319 Degrees of Freedom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

In the video we just saw we performed logarithmic regression for the height of a tree in feet over time and found our model equation to be y 2 062 7 695 In a where a is time in years According to this model how many years will it take for the tree to grow to 30 feet tall Round your answer to the nearest tenth of a year and do not include units Provide your answer below

Determine the total area under the standard normal curve for parts a through c below For each be sure to draw a standard normal curve and shade the area that is to be found Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 a Determine the total area under the standard normal curve to the left of z 2 or to the right of z 2 Draw a standard normal curve and shade the area that is to be found Choose the correct graph below Click here to view graph a Click here to view graph d Click here to view graph c O Click here to view graph b O The total area under the standard normal curve to the left of z 2 or to the right of z 2 is Round to four decimal places as needed b Determine the total area under the standard normal curve to the left of z 1 24 or to the right of z 2 24 Draw a standard normal curve and shade the area that is to be found Choose the correct graph below O Click here to view graph a Click here to view graph b Click here to view graph c

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 C at the freezing point of water Tests on a large sample of these thermometers reveal that at the freezing point of water some give readings below 0 C denoted by negative numbers and some give reading above 0 C denoted by positive numbers Assume that the mean reading is 0 C and the standard deviation of the readings is 1 00 C Also assume that the frequency distribution of errors closely resembles the normal distribution A thermometer is randomly selected and tested Find the temperature reading corresponding to the given information 12 Find P96 the 96th percentile 3

Which of the following are criteria for a binomial probability experiment Select all that apply A There are two mutually exclusive outcomes success or failure B The experiment is performed until a desired number of successes is reached C The experiment is performed a fixed number of times D The probability of success is the same for each trial of the experiment E The probability of success is different for each trial of the experiment F There are three mutually exclusive outcomes arriving on time arriving early and arriving late G Each trial depends on the previous trial H The trials are independent

According to a study conducted in one city 35 of adults in the city have credit card debts of more than 2000 A simple random sample of n 150 adults is obtained from the city Describe the sampling distribution of p the sample proportion of adults who have credit card debts of more than 2000 Round to three decimal places when necessary O A Exactly normal Hp 0 35 p 0 039 OB Binomial Hp 52 5 p 5 842 OC Approximately normal Hp 0 35 p 0 039 O D Approximately normal p 0 35 p 0 002

14 If 7 of the thermometers are rejected because they have readings that are too low but all other thermometers are acceptable find the temperature that separates the rejected thermometers from the others

What are the values of and o for the sampling distribution of the sample mean shown OA H 490 o 30 OB H 490 90 OC H 490 o 60 wwx 460 490 520

What is a random variable Choose the correct answer below OA A random variable is a numerical measure having either a finite or countable number of values of the ou of a probability experiment OB A random variable is a numerical measure having values that can be plotted on a line in an uninterrupted fashion of the outcome of a probability experiment OC A random variable is a numerical measure of the outcome of a probability experiment

Find the indicated value 15 20 005

Find the indicated probability 23 The diameters of bolts produced by a certain machine are normally distributed with a mean of 0 30 inches and a standard deviation of 0 01 inches What percentage of bolts will have a diameter greater than 0 32 inches

According to government data the probability that an adult was never in a museum is 15 In a random survey of 10 adults what is the probability that two or fewer were never in a museum Round to the nearest thousandth O 0 800 O 0 820 0 200 0 002

Fill in the blank to complete the statement The notation za is the z score that the area under the standard normal curve to the right of zo is The notation za is the z score that the area under the standard normal curve to the right of zo is 18 X 1

The graph to the right is the uniform density function for a friend who is x minutes late Find the probability that the friend is at least 23 minutes late www The probability that the friend is at least 23 minutes late is Density 1 30 0 0 10 20 Time min 30 X

Determine P and o from the given parameters of the population and sample size 74 o 36 n 81

MODEL EXAMPLE https youtu be tQ2uuurC5RM 1 Suppose that 65 of the population gets a flu vaccine If 30 of those who were not vaccinated get the flu and 10 of those who were vaccinated still get the flu find the probability that a person was vaccinated given that they have the flu 8 pts Draw the square Venn diagram and its four rectangles find the areas needed to compute the probability See the example video

Suppose x is a uniform random variable with values ranging from 30 to 60 Find the probability that a randomly selected observation exceeds 42 0000 0 6 0 1 0 4 0 9

Determine the logarithmic regression of the data below using either a calculator or spreadsheet program Then estimate he y value when the value is 50 Round your answer to the nearest tenth Do not include units in your answer 25 333 32 263 48 169 54 158 67 55 79 9

Solve the problem Round to the nearest tenth unless indicated otherwise 19 In one region the September energy consumption levels for single family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh Find P45 which is the consumption level separating the bottom 45 from the top 55

10 The probability that z lies between 0 and 3 01 P 0 Z 3 01

If z is a standard normal variable find the probability 9 The probability that z is less than 1 13 P z 1 13

17 Find the area of the shaded region The graph depicts IQ scores of adults and those scores are normally distributed with a mean of 100 and a standard deviation of 15 as on the Wechsler test 40 50 60 70 80 90 100 110 120 130 140 150 160 170

35 A rare and deadly disease has a disease rate of 0 1 A screening test of the disease called DT is good in the sense that the accuracy of the test among healthy people is 97 while the accuracy among diseased people is 99 What is the overall accuracy of the test DT Further if a friend of yours diagnosed positively what is the chance that he she really don t have the disease

18 Find the indicated IQ score The graph depicts IQ scores of adults and those scores are normally distributed with a mean of 100 and a standard deviation of 15 as on the Wechsler test The shaded area under the curve is 0 10

Provide an appropriate response 16 Which of the following is true about the distribution of IQ scores b The S D 15 a The mean 1

B 15 There are 100 male birds and 300 female birds in birdhouse A and 300 males and 100 females in

Describe the sampling distribution of p Round to three decimal places when necessary N 25 000 n 550 p 0 7 OA Approximately normal Hp 0 7 p 0 092 O B Binomial Hp 385 op 10 747 OC Exactly normal Hp 0 7 p 0 020 O D Approximately normal Hp 0 7 op 0 020

Which of the following are properties of the normal curve Select all that apply A The area under the normal curve to the right of the mean is 1 B The graph of a normal curve is skewed right C The high point is located at the value of the mean D The area under the normal curve to the right of the mean is 0 5 E The graph of a normal curve is symmetric F The high point is located at the value of the standard deviation

Complete the sentence below denoted p is given by the formula where x is the number of individuals with a specified characteristic in a sample of n individuals The The specified characteristic in a sample of n individuals denoted p is given by the formula p where x is the number of individuals with a

Describe the sampling distribution of p Assume the size of the population is 20 000 n 500 p 0 394 Describe the shape of the sampling distribution of p Choose the correct answer below OA The shape of the sampling distribution of p is not normal because n 0 05N and np 1 p 10 OB The shape of the sampling distribution of po is approximately normal because n 0 05N and np 1 p 10 OC The shape of the sampling distribution of p is approximately normal because n 0 05N and np 1 p 10 OD The shape of the sampling distribution of p is not normal because n 0 05N and np 1 p 10 Determine the mean of the sampling distribution of p Round to three decimal places as needed Determine the standard deviation of the sampling distribution of p Round to three decimal places as needed GA

Fill in the blank According to the law of large numbers as more observations are added to the sample the difference between the sample mean and the population mean O remains about the same O tends to become smaller O is inversely affected by the data added tonde to become largor

ect the correct choice that completes the sentence below

mean 0 and standard deviation 1 7 Shaded area is 0 9599 8 Shaded area is 0 0694 2 z Z with

Which of the following are properties of a probability density function pdf Select all that apply A The total area under the graph of the equation over all possible values of the random variable must equal 1 B The high point of the graph must be at the value of the population standard deviation o C The height of the graph of the equation must be greater than or equal to 0 for all possible values of the rando variable D The values of the random variable must be greater than or equal to 0 E The graph of the probability density function must be symmetric F The probability that x takes on any single individual value is greater than 0