*o use the values on the attached table to solve problems relatedto normal distribution.In a supermarket, the weight of apples has an approximately normal distribution with the mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an approximately normal distribution with the mean of 210 gram and the standard deviation of 15 gram.(a) When an apple and a pear are randomly selected, what is the probability that the apple weights more than the pear?(b) If Tom randomly buys 30 apples and 20 pears, what is the probability that their total weight exceeds 10kg (10kg = 10, 000g)? Table of the Standard Normal Cumulative Distribution Function &(z).0908.0790.05.04.03.02.01.00.00.01.02.03.04.05.06.07.08.09.00003 .00003 .00004 .00004 |.00004 .00004 .00004 .00004 .00005 |.00005.00005 .00005.00005 .00006 .00006 .00006 .00006 .00007 .00007 .00007.00008 .00008 |.00008 .00008 | .00009 .00009 .00010 .00010 .00010 |.00011.00011 .00012.00012 .00013 .00013 .00014.00014 .00015 |.00015 |.00016.00017 .00017 .00018 |.00019 .00019 |.00020 .00021 |.00022 .00022 |.00023.00024 .00025.00026 .00027 .00028 .00029 .00030 .00031 .00032 .00034.00035 .00036.00038 .00039 .00040 .00042 .00043 .00045 |.00047 .00048.00050 .00052.00054 .00056 .00058 .00060 .00062 .00064 |.00066 .00069.00071 .00074.00076 .00079 .00082 .00084 .00087 .00090 .00094 .00097.00100 .00104 |.00107 .00111 |.00114 | .00118 .00122 | .00126 |.00131 |.00135.00139 .00144.00149 .00154 .00159 .00164.00169 .00175 .00181 .00187.00193 .00199.00205 .00212 .00219 .00226 .00233 .00240 |.00248 .00256.00264 .00272.00280 .00289 .00298 .00307 .00317 .00326 .00336 .00347.00357 .00368 |.00379 | .00391 |.00402 | .00415| .00427 |.00440 |.00453 .00466.00480 .00494.00508 .00523 .00539 | .00554 .00570 |.00587 .00604 |.00621.00639 .00657.00676 .00695 .00714 .00734.00755 |.00776 |.00798 |.00820.00842 .00866|.00889 .00914 .00939 .00964 .00990 .01017 .01044 .01072.01101 .01130 .01160 .01191 .01222 .01255 .01287 .01321 .01355 .01390.01426 .01463.01500 .01539 .01578 .01618 .01659 .01700 .01743 .01786.01831 .01876.01923 | .01970 .02018 | .02068 .02118 | .02169 | .02222 |.02275.02330 .02385 .02442 .02500 |.02559 | .02619|.02680 |.02743 .02807 |.02872.02938 .03005 |.03074 .03144 |.03216 | .03288 .03362 .03438 .03515 |.03593.03673 .03754.03836 |.03920 |.04006 |.04093 .04182 |.04272 .04363 |.04457.04551 .04648.04746 .04846 .04947 .05050 .05155 .05262 .05370 .05480.50000 .50399.50798 .51197.51595 .51994.52392 .52790 .53188 .53586.53983 .54380.54776 .55172 .55567 .55962.56356 .56749 .57142 .57535.57926 .58317.58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409.61791 .62172.62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173.65542 .65910.66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793.69146 .69497 .69847|.70194.70540 |.70884.71226|.71566 | .71904 |.72240.72575 .72907.73237 | .73565 .73891 .74215 .74537 .74857 .75175 .75490.75804 .76115 .76424|.76730|.77035 | .77337 |.77637|.77935 |.78230 |.78524.78814 .79103.79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327.81594 .81859 .82121 .82381 .82639 | .82894 .83147 .83398 .83646 .83891.84134 .84375.84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214.86433 .86650 .86864 .87076 .87286 .87493 .87698 | .87900 |.88100 |.88298.88493 .88686.88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147.90320 .90490.90658 .90824 .90988 | .91149 | .91309 .91466 .91621 | .91774.91924 .9207392220 | .92364 |.92507| .92647 | .92785 | .92922 | .93056 | .93189.93319 .93448 .93574 .93699 |.93822| .93943 .94062 | .94179 | .94295 |.94408.94520 .94630.94738 .94845 .94950 95053 .95154 .95254 .95352 .95449.95543 .95637|.95728| .95818 | .95907| .95994 |.96080 .96164 |.96246 |.96327.96407 .96485.96562 .96638 .96712 .96784 .96856 96926 96995 .97062.97128 .97193 .97257 .97320|.97381| .97441.97500 | .97558 .97615 |.97670.97725 .97778.97831 .97882 .97932 97982 .98030 98077 98124 .98169.98214 .98257 .98300 .98341 .98382 .98422 .98461 |.98500 |.98537 |.9857498610 .9864598679 .98713 .98745 .98778 98809 .98840 98870 .98899.98928 98956.98983 | .99010 |.99036 | .99061 | .99086 | .99111 |.99134 | .99158.99180 .99202 .99224 .99245 .99266 .99286 .99305 .99324 .99343 .99361.99379 .99396.99413 .99430 .99446 .99461 .99477 .99492 .99506 .99520.99534 .99547.99560 .99573 .99585 .99598 .99609 |.99621 | .99632 |.99643.99653 .99664 .99674 .99683 .99693 .99702 .99711 .99720 .99728 .9973699744 9975299760 99767 .99774 .99781 .99788 .99795 .99801 .99807.99813 .99819.99825 .99831 .99836 .99841 .99846 99851 .99856 .9986199865 9986999874 .99878 .99882 |.99886 .99889 | .99893 |.99896 |.99900.99903 .99906.99910 .99913 .99916 .99918 .99921 .99924 .99926 .99929.99931 .99934.99936 .99938 .99940 .99942 .99944 .99946 .99948 .99950.99952 .99953 .99955 .99957 .99958| .99960 |.99961|.99962 .99964 .99965.99966 .99968.99969 .99970 .99971 .99972 .99973 .99974 .99975 .99976.99977 .99978.99978 .99979 .99980 .99981 .99981 | .99982 .99983 .99983.99984 .99985.99985 .99986 .99986 .99987 .99987 .99988 .99988 .99989.99989 .99990 .99990 .99990 .99991|.99991.99992 | .99992 .99992 |.99992.99993 .99993.99993 .99994 .99994 99994 .99994 99995 99995 .99995.99995 .99995|.99996 | .99996 |.99996 | .99996 | .99996 | .99996 | .99997 | .99997-3.90.0-3.80.1-3.70.2-3.60.3-3.50.4-3.40.5-3.30.6-3.20.7-3.10.8-3.00.9-2.91.0-2.81.1-2.71.2-2.61.3-2.51.4-2.41.5-2.31.6-2.21.7-2.11.8-2.01.9-1.92.0-1.82.1-1.72.2-1.6.05592 .05705.05821 .05938 .06057 .06178 .06301 .06426 .06552 .06681.06811 .06944.07078 .07215 .07353 | .07493 .07636 |.07780 |.07927 |.08076.08226 .08379.08534 .08691 .08851 .09012 .09176 .09342 .09510 .09680.09853 .10027.10204 |.10383 .10565 .10749 |.10935 |.11123 |.11314 |.11507.11702 .11900.12100 |.12302|.12507 |.12714.12924 |.13136 .13350 |.13567.13786 .14007.14231 |.14457.14686 .14917 .15151 |.15386 .15625 .15866.16109|.16354.16602 .16853.17106 .17361.17619 .17879 .18141 .18406.18673 | .18943 |.19215|.19489.19766 | .20045 .20327|.20611 .20897|.21186.21476 .21770 .22065 .22363 .22663 .22965 .23270 .23576 .23885 .24196.24510 .24825.25143 .25463 .25785 .26109 .26435 .26763| .27093 | .27425.27760 .28096 .28434 |.28774| .29116 |.29460 .29806 .30153 | .30503 | .30854.31207 .31561|.31918| .32276 |.32636|.32997.33360 |.33724 .34090 |.34458.34827 .35197|.35569 .35942.36317|.36693 .37070 .37448 .37828| .38209.38591 .38974| .39358 | .39743 | .40129 | .40517 | .40905 | .41294 | .41683 .42074.42465 .42858| 43251 | .43644 |.44038 | .44433 44828 .45224 .45620 | .46017.46414 .46812 47210| .47608 .48006 | .48405 | .48803 | .49202 | .49601 .500002.3-1.52.4-1.42.5-1.32.6-1.22.7-1.12.8-1.02.9-0.93.0-0.83.1-0.73.2-0.63.3-0.53.4-0.43.5-0.33.6-0.23.7-0.13.8-0.03.9

a) Consider X-Weight of apples and Y-Weight of pears. Then, X~N(190,144)Y~N(210,225) Consider,…

e values on the attached table to solve problems related to normal distribution. In a supermarket, the weight of apples has an approximately normal distribution with the mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an approximately normal distribution with the mean of 210 gram and the standard deviation of 15 gram. (a) When an apple and a pear are randomly selected, what is the probability that the apple weights more than the pear? (b) If Tom randomly buys 30 apples and 20 pears, what is the probability that their total weight exceeds 10kg (10kg = 10, 000

e values on the attached table to solve problems related to normal distribution. In a supermarket, the weight of apples has an approximately normal distribution with the mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an approximately normal distribution with the mean of 210 gram and the standard deviation of 15 gram. (a) When an apple and a pear are randomly selected, what is the probability that the apple weights more than the pear? (b) If Tom randomly buys 30 apples and 20 pears, what is the probability that their total weight exceeds 10kg (10kg = 10, 000

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Information needed for the next two problems: A bored statistician is interested in researching length of commercial breaks on cable channels (ESPN, TNT, etc.) and comparing them to the length of commercial breaks on the networks (ABC, CBS, NBC, FOX). She times a random sample of commercials from each of the two types of broadcasts which are assumed to be normally distributed. Source n Mean(min.) Std. Dev. (min.) Cable 15 2.36 0.16 Network 12 2.18 0.13 Based on your previous answer for the upper bound and assuming the lower bound ratio of variances of cable to network is 0.5531, your conclusion about the spread of the variances of cable vs network commercials is O 1 is in the interval so statistically the same O O is in the interval so statistically the same O 1 is not in the interval so statistically different O O is in the interval so statistically not the same O 1 is in the interval so statistically not the same
Alex wants to find out: if the standard deviation of the mean for the sampling distribution of random samples of size 256 from a large or infinite population is 9, how large must the sample size become if the standard deviation is to be reduced to 2.7 (or even smaller)?
Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true? The dispersions of the distributions are different. The dispersions of the distributions are the same. The distributions are from two different families of distributions. The locations of the distributions are different.
A population of N = 5 scores has a mean of u = 20 and a standard deviation of o = 4. Which of the following is the correct Interpretation of the standard deviation? O The average distance of scores from the mean of p- 20 is 5 points. O The average distance of scores from the mean of u = 20 is 1 point. The average distance of scores from the mean of u = 20 is 4 points. O The average squared distance of scores from the mean of u = 20 is 4 points.
A collection of numbers is Normal with a Mean of 20 and a Standard Deviation of 5; that is N(20,5). Boris’s score is 23.7 and Bela’s score is 26.2. What is the probability that a score is greater than Boris and less than Bela? Your final answer should be correct to 3 places after the decimal point. ________
No written by hand solution
B Choosing a topic Sk.. For data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula 1 where p is the minimum percentage of scores that fall within k k2 is p = 1 - standard deviations on both sides of the mean. Use this formula to answer the following questions. a) If you have scores and you don't know if they are normally distributed, find the minimum percentage of scores that fall within 2.2 standard deviations on both sides of the mean? b) If you have scores that are normally distributed, find the percentage of scores that fall within 2.2 standard deviations on both sides of the mean? c) If you have scores and you don't know if they are normally distributed, how many standard deviations on both sides of the mean do we need to go to have 64 percent of the scores? Note: To answer part c you will need to solve the equation for k.
Which of the following is the best statement of the Law of Large Numbers? If the parent population (from which the data are drawn) is normally distributed, then the sample mean, , will follow a normal distribution. For bell-shaped data, approximately 68% of the data will be within one standard deviation of the mean, about 95% of the data will be within two standard deviations of the mean, and approximately 99.7% of the data will be within three standard deviations of the mean. If the sample size is large, the sample mean will be close to the population mean µ If the sample size is large, the shape of the sampling distribution of the sample mean will be approximately normal.