A simple random sample of size n 36 is obtained from a population that is skewed right with 81 and 18 (a) Describe the sampling distribution of x (b) What is P (x 84 6) (c) What is P (x73 65) (d) What is P (77 1 A simple random sample of size n 37 is obtained from a population with 65 and 19 (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean Assuming that this condition is true, describe the sampling distribution of x (b) Assuming the normal model can be used, determine P(x 68 6) (c) Assuming the normal model can be used, determine P(x 66 6) (a) What must be true regarding the distribution of the population A Since the sample size is large enough, the population distribution does not need to be normal OB The population must be normally distributed and the sample size must be large C The population must be normally distributed OD The sampling distribution must be assumed to be normal Assuming the normal model can be used, describe the sampling distribution x Choose the correct answer below OA Approximately normal, with 65 and 19 x B Approximately normal, with x 65 and OC Approximately normal, with 65 and 19 37 37 x 19 (b) P(x 68 6) (Round to four decimal places as needed ) (c) P(x 66 6) (Round to four decimal places as needed ) The shape of the distribution of the time required to get an oil change at a 15 minute oil change facility is skewed right However, records indicate that the mean time is 16 2 minutes, and the standard deviation is 3 5 minutes Complete parts (a) through (c) (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required A The sample size needs to be less than or equal to 30 B Any sample size could be used C The normal model cannot be used if the shape of the distribution is skewed right D The sample size needs to be greater than or equal to 30 (b) What is the probability that a random sample of n 40 oil changes results in a sample mean time less than 15 minutes The probability is approximately (Round to four decimal places as needed ) (c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal On a typical Saturday, the oil change facility will perform 40 oil changes between 10 A M and 12 P M Treating this as a random sample, there would be a 10 chance of the mean oil change time being at or below what value This will be the goal established by the manager There is a 10 chance of being at or below a mean oil change time of (Round to one decimal place as needed ) minutes The acceptable level for insect filth in a certain food item is 4 insect fragments (larvae, eggs, body parts, and so on) per 10 grams A simple random sample of 40 ten gram portions of the food item is obtained and results in a sample mean of x 4 9 insect fragments per ten gram portion Complete parts (a) through (c) below (a) Why is the sampling distribution of x approximately normal A The sampling distribution of x is approximately normal because the population is normally distributed and the sample size is large enough B The sampling distribution of x is assumed to be approximately normal C The sampling distribution of x is approximately normal because the sample size is large enough D The sampling distribution of x is approximately normal because the population is normally distributed (b) What is the mean and standard deviation of the sampling distribution of x assuming 4 and Px (Round to three decimal places as needed ) (Round to three decimal places as needed ) (c) What is the probability a simple random sample of 40 ten gram portions of the food item results in a mean of at least 4 9 insect fragments P(x 4 9) (Round to four decimal places as needed ) this result unusual A This result is unusual because its probability is small OB This result is unusual because its probability is large C This result is not unusual because its probability is small OD This result is not unusual because its probability is large What might we conclude A Since this result is not unusual, it is reasonable to conclude that the population mean is higher than 4 B Since this result is not unusual, it is not reasonable to conclude that the population mean is higher than 4 C Since this result is unusual, it is not reasonable to conclude that the population mean is higher than 4 D Since this result is unusual, it is reasonable to conclude that the population mean is higher than 4 Suppose a simple random sample of size n 75 is obtained from a population whose size is N 30,000 and whose population proportion with a specified characteristic is p 0 4 Complete parts (a) through (c) below (a) Describe the sampling distribution of p Choose the phrase that best describes the shape of the sampling distribution below A Not normal because n0 05N and np(1 p) 10 B Approximately normal because n 0 05N and np(1 p) 10 C Approximately normal because n 0 05N and np(1 p) 10 D Not normal because n 0 05N and np(1 p) 10 Determine the mean of the sampling distribution of p (Round to one decimal place as needed ) Determine the standard deviation of the sampling distribution of p (Round to six decimal places as needed ) (b) What is the probability of obtaining x 36 or more individuals with the characteristic That is, what is P(p 0 48) P(p 0 48) (Round to four decimal places as needed ) (c) What is the probability of obtaining x 21 or fewer individuals with the characteristic That is, what is P(p 0 28) P(p 0 28) (Round to four decimal places as needed ) Suppose a simple random sample of size n 1000 is obtained from a population whose size is N 1,000,000 and whose population proportion with a specified characteristic is p 0 48 Complete parts (a) through (c) below (a) Describe the sampling distribution of p OA Approximately normal, 0 48 and 0 0005 B Approximately normal, 0 48 and o 0 0158 p p OC Approximately normal, p 0 48 and 0 0002 p (b) What is the probability of obtaining x 520 or more individuals with the characteristic P(x 520) (Round to four decimal places as needed ) (c) What is the probability of obtaining x 450 or fewer individuals with the characteristic P(X 450) (Round to four decimal places as needed ) Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000) An exit poll of 400 voters finds that 196 voted for the referendum How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0 52 Based on your result, comment on the dangers of using exit polling to call elections How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0 52 The probability that fewer than 196 people voted for the referendum is (Round to four decimal places as needed ) Comment on the dangers of using exit polling to call elections Choose the correct answer below A The result is not unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5 Thus, it is not unusual for a wrong call to be made in an election if exit polling alone is considered B The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5 Thus, it is not unusual for a wrong call to be made in an election if exit polling alone is considered The result is unusual because the probability that p is equal to or more extreme than the sample proportion is less than 5 Thus, it is unusual for a wrong call to be made in an election if exit polling alone is considered D The result is not unusual because the probability that p is equal to or more extreme than the sample proportion is less than 5 Thus, it is unusual for a wrong call to be made in an election if exit polling alone is considered Standard Normal Distribution Table (page 1) Area Standard Normal Distribution D Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 3 4 0 0003 0 0003 0 0003 0 0003 0 0003 0 0003 0 0003 0 0003 0 0003 0 0002 3 3 0 0005 0 0005 0 0005 0 0004 0 0004 0 0004 0 0004 0 0004 0 0004 0 0003 3 2 0 0007 0 0007 0 0006 0 0006 0 0006 0 0006 0 0006 0 0005 0 0005 0 0005 3 1 0 0010 0 0009 0 0009 0 0009 0 0008 0 0008 0 0008 0 0008 0 0007 0 0007 3 0 0 0013 0 0013 0 0013 0 0012 0 0012 0 0011 0 0011 0 0011 0 0010 0 0010 29 0 0019 0 0018 0 0018 0 0017 0 0016 0 0016 0 0015 0 0015 0 0014 0 0014 2 8 0 0026 0 0025 0 0024 0 0023 0 0023 0 0022 0 0021 0 0021 0 0020 0 0019 2 7 0 0035 0 0034 0 0033 0 0032 0 0031 0 0030 0 0029 0 0028 0 0027 0 0026 2 6 0 0047 0 0045 0 0044 0 0043 0 0041 0 0040 0 0039 0 0038 0 0037 0 0036 2 5 0 0062 0 0060 0 0059 0 0057 0 0055 0 0054 0 0052 0 0051 0 0049 0 0048 2 4 0 0082 0 0080 0 0078 0 0075 0 0073 0 0071 0 0069 0 0068 0 0066 0 0064 2 3 0 0107 0 0104 0 0102 0 0099 0 0096 0 0094 0 0091 0 0089 0 0087 0 0084 2 2 0 0139 0 0136 0 0132 0 0129 0 0125 0 0122 0 0119 0 0116 0 0113 0 0110 2 1 0 0179 0 0174 0 0170 0 0166 0 0162 0 0158 0 0154 0 0150 0 0146 0 0143 2 0 0 0228 0 0222 0 0217 0 0212 0 0207 0 0202 0 0197 0 0192 0 0188 0 0183 1 9 0 0287 0 0281 0 0274 0 0268 0 0262 0 0256 0 0250 0 0244 0 0239 0 0233 1 8 0 0359 0 0351 0 0344 0 0336 0 0329 0 0322 0 0314 0 0307 0 0301 0 0294 1 7 0 0446 0 0436 0 0427 0 0418 0 0409 0 0401 0 0392 0 0384 0 0375 0 0367 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 1 4 0 0808 0 0793 0 0778 0 0764 0 0749 0 0735 0 0721 0 0708 0 0694 0 0681 1 3 0 0968 0 0951 0 0934 0 0918 0 0901 0 0885 0 0869 0 0853 0 0838 0 0823 1 2 0 1151 0 1131 0 1112 0 1093 0 1075 0 1056 0 1038 0 1020 0 1003 0 0985 1 1 0 1357 0 1335 0 1314 0 1292 0 1271 0 1251 0 1230 0 1210 0 1190 0 1170 1 0 0 1587 0 1562 0 1539 0 1515 0 1492 0 1469 0 1446 0 1423 0 1401 0 1379 0 9 0 1841 0 1814 0 1788 0 1762 0 1736 0 1711 0 1685 0 1660 0 1635 0 1611 0 8 0 2119 0 2090 0 2061 0 2033 0 2005 0 1977 0 1949 0 1922 0 1894 0 1867 0 7 0 2420 0 2389 0 2358 0 2327 0 2296 0 2266 0 2236 0 2206 0 2177 0 2148 0 6 0 2743 0 2709 0 2676 0 2643 0 2611 0 2578 0 2546 0 2514 0 2483 0 2451 0 5 0 3085 0 3050 0 3015 0 2981 0 2946 0 2912 0 2877 0 2843 0 2810 0 2776 0 4 0 3446 0 3409 0 3372 0 3336 0 3300 0 3264 0 3228 0 3192 0 3156 0 3121 0 3 0 3821 0 3783 0 3745 0 3707 0 3669 0 3632 0 3594 0 3557 0 3520 0 3483 0 2 0 4207 0 4168 0 4129 0 4090 0 4052 0 4013 0 3974 0 3936 0 3897 0 3859 0 1 0 4602 0 4562 0 4522 0 4483 0 4443 0 4404 0 4364 0 4325 0 4286 0 4247 0 0 0 5000 0 4960 0 4920 0 4880 0 4840 0 4801 0 4761 0 4721 0 4681 0 4641 Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 Standard Normal Distribution Table (page 2) Area n Standard Normal Distribution Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 0 0 5000 0 5040 0 5080 0 5120 0 5160 0 5199 0 5239 0 5279 0 5319 0 5359 0 1 0 5398 0 5438 0 5478 0 5517 0 5557 0 5596 0 5636 0 5675 0 5714 0 5753 0 2 0 5793 0 5832 0 5871 0 5910 0 5948 0 5987 0 6026 0 6064 0 6103 0 6141 0 3 0 6179 0 6217 0 6255 0 6293 0 6331 0 6368 0 6406 0 6443 0 6480 0 6517 0 4 0 6554 0 6591 0 6628 0 6664 0 6700 0 6736 0 6772 0 6808 0 6844 0 6879 0 5 0 6915 0 6950 0 6985 0 7019 0 7054 0 7088 0 7123 0 7157 0 7190 0 7224 0 6 0 7257 0 7291 0 7324 0 7357 0 7389 0 7422 0 7454 0 7486 0 7517 0 7549 0 7 0 7580 0 7611 0 7642 0 7673 0 7704 0 7734 0 7764 0 7794 0 7823 0 7852 0 8 0 7881 0 7910 0 7939 0 7967 0 7995 0 8023 0 8051 0 8078 0 8106 0 8133 0 9 0 8159 0 8186 0 8212 0 8238 0 8264 0 8289 0 8315 0 8340 0 8365 0 8389 2 1 2 3 2 5 2 6 2 8 2 9 3 0 3 1 3 2 3 3 ECCE CCEECECCE E 1 0 0 8413 0 8438 0 8461 0 8485 0 8508 0 8531 0 8554 0 8577 0 8599 0 8621 1 1 0 8643 0 8665 0 8686 0 8708 0 8729 0 8749 0 8770 0 8790 0 8810 0 8830 1 2 0 8849 0 8869 0 8888 0 8907 0 8925 0 8944 0 8962 0 8980 0 8997 0 9015 1 3 0 9032 0 9049 0 9066 0 9082 0 9099 0 9115 0 9131 0 9147 0 9162 0 9177 1 4 0 9192 0 9207 0 9222 0 9236 0 9251 0 9265 0 9279 0 9292 0 9306 0 9319 1 5 0 9332 0 9345 0 9357 0 9370 0 9382 0 9394 0 9406 0 9418 0 9429 0 9441 1 6 0 9452 0 9463 0 9474 0 9484 0 9495 0 9505 0 9515 0 9525 0 9535 0 9545 1 7 0 9554 0 9564 0 9573 0 9582 0 9591 0 9599 0 9608 0 9616 0 9625 0 9633 1 8 0 9641 0 9649 0 9656 0 9664 0 9671 0 9678 0 9686 0 9693 0 9699 0 9706 1 9 0 9713 0 9719 0 9726 0 9732 0 9738 0 9744 0 9750 0 9756 0 9761 0 9767 2 0 0 9772 0 9778 0 9783 0 9788 0 9793 0 9798 0 9803 0 9808 0 9812 0 9817 0 9821 0 9826 0 9830 0 9834 0 9838 0 9842 0 9846 0 9850 0 9854 0 9857 2 2 0 9861 0 9864 0 9868 0 9871 0 9875 0 9878 0 9881 0 9884 0 9887 0 9890 0 9893 0 9896 0 9898 0 9901 0 9904 0 9906 0 9909 0 9911 0 9913 0 9916 2 4 0 9918 0 9920 0 9922 0 9925 0 9927 0 9929 0 9931 0 9932 0 9934 0 9936 0 9938 0 9940 0 9941 0 9943 0 9945 0 9946 0 9948 0 9949 0 9951 0 9952 0 9953 0 9955 0 9956 0 9957 0 9959 0 9960 0 9961 0 9962 0 9963 0 9964 2 7 0 9965 0 9966 0 9967 0 9968 0 9969 0 9970 0 9971 0 9972 0 9973 0 9974 0 9974 0 9975 0 9976 0 9977 0 9977 0 9978 0 9979 0 9979 0 9980 0 9981 0 9981 0 9982 0 9982 0 9983 0 9984 0 9984 0 9985 0 9985 0 9986 0 9986 0 9987 0 9987 0 9987 0 9988 0 9988 0 9989 0 9989 0 9989 0 9990 0 9990 0 9990 0 9991 0 9991 0 9991 0 9992 0 9992 0 9992 0 9992 0 9993 0 9993 0 9993 0 9993 0 9994 0 9994 0 9994 0 9994 0 9994 0 9995 0 9995 0 9995 0 9995 0 9995 0 9995 0 9996 0 9996 0 9996 0 9996 0 9996 0 9996 0 9997 3 4 0 9997 0 9997 0 9997 0 9997 0 9997 0 9997 0 9997 0 9997 0 9997 0 9998 Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09

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Question: A simple random sample of size n = 36 is obtained from a population that is skewed right with = 81 and = 18.

A simple random sample of size n = 36 is obtained from a population that is skewed right with = 81 and = 18. (a) Describe the sampling distribution of x. (b) What is P (x > 84.6)? (c) What is P (x73.65)? (d) What is P (77.1 a population with =65 and = 19. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x. (b) Assuming the normal

A simple random sample of size n = 36 is obtained from a population that is skewed right with = 81 and = 18. (a) Describe the sampling distribution of x. (b) What is P (x > 84.6)? (c) What is P (x73.65)? (d) What is P (77.1 A simple random sample of size n = 37 is obtained from a population with =65 and = 19. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x. (b) Assuming the normal model can be used, determine P(x

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